Answer: In Figure 9, the distance from A to D is y, the distance from D to C is x, and

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.IfA = 42 and c = 15 ft, find a.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.IfA = 42 and c = 89 cm, find b.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.If A = 34 and a = 22 m, find c.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.IfA 34 and b = 55 m, find c.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.IfB 24.so and c 2.34 ft, find a.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.IfB 16.9 and c 7.55 cm, find b.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.IfB = 55.33 and b = 12.34 yd, find a.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.If B = 77.66 and a = 43.21 inches, find b.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.If a = 16 cm and b = 26 cm, findA.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.If a = 42.3 inches and b = 32.4 inches, find B.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.If b 6.7 m and c 7.7 m, findA.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.If b 9.8 mm and c 12 mm, find B.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.If c 45.54 ft and a = 23.32 ft, find B.

Problems I through 14 refer to right triangle ABC with C 90. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Also, write your answers for angles in decimal degrees.If c = 5.678 ft and a = 4.567 ft, find A.

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)A = 25, c = 24 m

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)A = 41, c = 36 m

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)A 32.6, a = 43.4 inches

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)A 48.3, a 3.48 inches

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)A = 10 42', b = 5.932 cm

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)A 66 54', b 28.28 cm

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)B = 76, C = 5.8 ft

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)B = 21, C 4.2ft

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)B = 26 30', b = 324 mm

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)B 53 30', b 725 mm

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)B = 23.45, a = 5.432 mi

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)B 44.44, a 5.555 mi

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)a = 37 ft, b = 87 ft

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)a 91 ft, b 85 ft

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)a = 2.75 cm, C = 4.05 cm

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)a = 2.75 cm, C = 4.05 cm

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)b = 12.21 inches, C = 25.52 inches

Problems 15 through 32 refer to right triangle ABC with C 90. In each case, solve for all the missing parts using the given information. (In Problems 27 through 32, write your angles in decimal degrees.)b 377.3 inches, c 588.5 inches

In Problems 33 and 34, use the infonnation given in the diagram to find A to the the nearest degree .

In Problems 33 and 34, use the infonnation given in the diagram to find A to the the nearest degree .

The circle in Figure 7 has a radius of r and center at C. The distance from A to B is x. For Problems 35 through 38, redraw Figure 7, label it as indicated in each problem, D and then solve the problem.IfA = 31 and r = 12, find x.

The circle in Figure 7 has a radius of r and center at C. The distance from A to B is x. For Problems 35 through 38, redraw Figure 7, label it as indicated in each problem, D and then solve the problem.If C = 26 and r = 19, find x.

The circle in Figure 7 has a radius of r and center at C. The distance from A to B is x. For Problems 35 through 38, redraw Figure 7, label it as indicated in each problem, D and then solve the problem.If If A C = = 45 x = = 15, find r.

The circle in Figure 7 has a radius of r and center at C. The distance from A to B is x. For Problems 35 through 38, redraw Figure 7, label it as indicated in each problem, D and then solve the problem.If A C = 65 and x = 22, find r.

Figure 8 shows two right triangles drawn at 90 to each other. For Problems 39 through 42, redraw Figure 8, label it as the problem indicates, and then solve the problem.If LABD = 27, C = 62, and BC = 42, find x and then find h.

Figure 8 shows two right triangles drawn at 90 to each other. For Problems 39 through 42, redraw Figure 8, label it as the problem indicates, and then solve the problem.If LABD = 53, C = 48, and BC = 42, find x and then find h.

Figure 8 shows two right triangles drawn at 90 to each other. For Problems 39 through 42, redraw Figure 8, label it as the problem indicates, and then solve the problem.IfAC = 32, h = 19, and C = 41, find LABD.

Figure 8 shows two right triangles drawn at 90 to each other. For Problems 39 through 42, redraw Figure 8, label it as the problem indicates, and then solve the problem.IfAC = 19, h = 32, and C = 49, find LABD.

In Figure 9, the distance from A to D is y, the distance from D to C is x, and the dish tance from C to B is h. Use Figure 9 to solve Problems 43 through 48.IfA = 41, LBDC = 58,AB = 18, and DB = 14, find x, theny.

In Figure 9, the distance from A to D is y, the distance from D to C is x, and the dish tance from C to B is h. Use Figure 9 to solve Problems 43 through 48.IfA = 32, LBDC = 48, AB = 17, and DB = 12, find x, then y.

In Figure 9, the distance from A to D is y, the distance from D to C is x, and the dish tance from C to B is h. Use Figure 9 to solve Problems 43 through 48.IfA = 41 0, LBDC = 58, and AB = 28, find h, then x.

In Figure 9, the distance from A to D is y, the distance from D to C is x, and the dish tance from C to B is h. Use Figure 9 to solve Problems 43 through 48.IfA = 32, LBDC = 48, and AB = 56, find h, then x.

In Figure 9, the distance from A to D is y, the distance from D to C is x, and the dish tance from C to B is h. Use Figure 9 to solve Problems 43 through 48.IfA = 43, LBDC = 57, andy = ll,findx.

In Figure 9, the distance from A to D is y, the distance from D to C is x, and the dish tance from C to B is h. Use Figure 9 to solve Problems 43 through 48.IfA = 32, LBDC = 41, andy = 14, findx.

Suppose each edge ofthe cube shown in Figure 10 is 5.00 inches long. Find the A~ measure of the angle fonned by diagonals CF and CH. Round your answer to the nearest tenth of a degree

Suppose each edge of the cube shown in Figure 10 is 3.00 inches long. Find the I ve measure of the angle fonned by diagonals DE and DG. Round your answer to 2, H l/ql--f the nearest tenth of a degree.

Suppose each edge of the cube shown is x inches long. Find the measure of the c D angle formed by diagonals CF and CH in Figure 10. Round your answer to the Figure 10 nearest tenth of a degree.

Soccer A regulation soccer field has a rectangular penalty area that measures 132 feet ~J by 54 feet. The goal is 24 feet wide and centered along the back of the penalty area. Assume the goalkeeper can block a shot 6 feet to either side of their position for a total coverage of 12 feet. (Source: Federation lntemationale de Football Association)A penalty kick is taken from a comer of the penalty area at position A (see Figure 11). The goalkeeper stands 6 feet from the goalpost nearest the shooter and can thus block a shot anywhere between the middle of the goal and the nearest goalpost (segment CD). To score, the shooter must kick the ball within the angle CAE. Find the measure of this angle to the nearest tenth of a degree. 24ft Figure 11

Soccer A regulation soccer field has a rectangular penalty area that measures 132 feet ~J by 54 feet. The goal is 24 feet wide and centered along the back of the penalty area. Assume the goalkeeper can block a shot 6 feet to either side of their position for a total coverage of 12 feet. (Source: Federation lntemationale de Football Association)A penalty kick is taken from a comer of the penalty area at position A (see Figure 12). The goalkeeper stands in the center of the goal and can thus block a shot anywhere along segment CD. To score, the shooter must kick the ball within the angle CAE or angle DAF. Find the sum of these two angles to the nearest tenth ofa degree. Figure 12

Soccer A regulation soccer field has a rectangular penalty area that measures 132 feet ~J by 54 feet. The goal is 24 feet wide and centered along the back of the penalty area. Assume the goalkeeper can block a shot 6 feet to either side of their position for a total coverage of 12 feet. (Source: Federation lntemationale de Football Association)A penalty kick is taken from the center of the penalty area at position A (see Figure 13). The goalkeeper stands in the center ofthe goal and can thus block a shot anywhere along segment CD. To score, the shooter must kick the ball within the angle CAE or angle DAF. Find the sum of these two angles to the nearest tenth ofa degree.

Soccer A regulation soccer field has a rectangular penalty area that measures 132 feet ~J by 54 feet. The goal is 24 feet wide and centered along the back of the penalty area. Assume the goalkeeper can block a shot 6 feet to either side of their position for a total coverage of 12 feet. (Source: Federation lntemationale de Football Association)Based on your answers to Problems 52 and 53, should the goalkeeper stand to the side or at the center of the goal? Why?

Soccer A regulation soccer field has a rectangular penalty area that measures 132 feet ~J by 54 feet. The goal is 24 feet wide and centered along the back of the penalty area. Assume the goalkeeper can block a shot 6 feet to either side of their position for a total coverage of 12 feet. (Source: Federation lntemationale de Football Association)Based on your answers to Problems 52 and 54, should the shooter kick from the corner or the center of the penalty area? Why?

Repeat Example 5 from this section for the following values of e.e = 30

Repeat Example 5 from this section for the following values of e.e = 60

Repeat Example 5 from this section for the following values of e.= 120

Repeat Example 5 from this section for the following values of e.= 135

Ferris Wheel In 1897, a Ferris wheel was built in Vienna that still stands today. [e] It is named the Riesenrad, which translates to the Great Wheel. The diameter of enth I the the Riesenrad is 197 feet. The top of the wheel stands 209 feet above the ground. Figure 14 is a model of the Riesenrad with angle e the central angle that is formed as a rider moves from the initial position Po to position Pl. The rider is h feet above the ground at position Pl. 3. Find h if eis 120.0. b. Find h if eis 210.0. c. Find h if eis 315.0

Ferris Wheel A Ferris wheel with a diameter of 165 feet was built in St. Louis in 1986. It is called Colossus. The top of the wheel stands 174 feet above the bot lig_ ground. Use the diagram in Figure 14 as a model of Colossus. the 3. Find h if eis 150.0. 11th b. Find h if eis 240.0. c. Find h if eis 315.0.

The following problems review material that we covered in Section 1.4. If sec B = 2, find cos2B.

The following problems review material that we covered in Section 1.4. If csc B = 3, find sin2 B

The following problems review material that we covered in Section 1.4. Ifsin e = 1/3 and etenninates in QI, find cos e.

The following problems review material that we covered in Section 1.4. If cos e -2/3 and eterminates in QIII, find sin e.

The following problems review material that we covered in Section 1.4. If cos A = 2/5 with A in QIV, find sin A.

The following problems review material that we covered in Section 1.4. Ifsin A = 114 with A in QII, find cos A.

Find the remaining trigonometric ratios for e, if sin e = V3/2 with (J in QII

Find the remaining trigonometric ratios for e, if cos e ltV'S with (J in QIV

Find the remaining trigonometric ratios for e, if sec e = -2 with (J in QIII

Find the remaining trigonometric ratios for e, if csc (J = -2 with (J in QIII

Human Cannonball In Example 2 of Section 1.2, we found the equation ofthe path of the human cannonbalL At the 1997 Washington County Fair in Oregon, David Smith, Jr., The Bullet, was shot from a cannon. As a human cannonball, he reached a height of 70 feet before landing in a net 160 feet from the cannon. In that example we found the equation that describes his path is 7 y= 80)2 + 70 for 0 x:O:; 160 Graph this equation using the window o x:O:; 180, scale 20; 0:0:; y:o:; 80, scale = 10 Then zoom in on the curve near the origin until the graph has the appearance of a straight line. Use ITRACE Ito find the coordinates of any point on the graph. This point defines an approximate right triangle (Figure 15). Use the triangle to find the angle between the cannon and the horizontal. y Figure 15 Figure 16

Human Cannonball To get a better estimate of the angle described in Problem 73, we can use the table feature of your calculator. From Figure 15, we see that for any point (x, y) on the curve, (J = tan-1 (y/x). Define functions Yl andY2 as shown in Figure 16. Then set up your table so that you can input the following values of x: x 10,5, 1,0.5,0.1,0.01 Based on the results, what is the angle between the cannon and the horizontal?