5.8 Notes MATH 113
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This 5 page Class Notes was uploaded by Katelynn Jones on Tuesday September 22, 2015. The Class Notes belongs to MATH 113 at University of Alabama - Tuscaloosa taught by Phylisicia carter in Fall 2015. Since its upload, it has received 21 views. For similar materials see - Precalculus Trigonometry in Mathematics (M) at University of Alabama - Tuscaloosa.
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Date Created: 09/22/15
Solving Right Triangles a t quota W s g 30thng a right triangle means nding the mishing lengths of its sides and the measurements of its angles We Will label right triangles so that side a is opposite angle A side I is opposite angle B and side c the hypotenuse is opposite of the right angle C When solving a right triangle we will use the sine cosine and tangent functions rather than their reciprocals Example 4 a f 4 m 3 v as H 39 451 L t Example Example Trigonometry iiin Bearings In navigation and surveying problems the term bearing is used to specify the location of one point relative to another The hearing from point 0 to point P is the acute angle measured in degrees between ray UP and a northnsouth line k VEEEs i The bearing from 0 to P can also be described using the phrase the bearing of P from O The gures below are examples of bearings The north south line and the eastwest line intersect at right angles quotan w a How to write a bearing r I If the acute angle is measured from the north side of the northsouth line then we write N rst If the acute angle is measured from the south side of the northsouth line then we write S rst U Second we writ the measure of the acute angle 0 If the acute angle is measured on the east side of the north south line then we write E last If the acute angle is measure on the west side of the north south line then we write W last Example Find the hearing from O to A 1 39 2 1 ii at 1 5 A 339 I A if t quotI iffy m L3 339 IT 34 its V i v air 39 I quotam 39 39 L Example The tallest television transmitting tower in the world is in North Dakota From a point on level ground 5280 feet one mile from the base of the tower the angle of elevation is 211 Approximate the height of the tower to the nearest foot DJ Example The Statue of Liberty is approximately 305 feet tall If the angle of elevation of a ship to the top of quothe statue is 226 how far to the nearest foot is the ship from the statue s base 3 Example A boat leaves the entrance to a harbor and travels 125 miles on a bearing of N 39 miles north and how many miles east from the harbor has the boat traveled its 7 w I it w Example A forest ranger sights a re directly to the south A second ranger 9 miles east of the rst ranger also sights the re The bearing from the second ranger is to the fire is S 34 W How far is the first ranger from the fire Example You leave your house it your bearing from your house Example A straight trail with a uniform inclination of l4 leads from a lodge at an elevation of 500 feet to a mountain lake at an elevation of 7100 feet What is the length of the trail to the nearest foot Example A radio transmission tower is 160 feet talL How long should a guy wire be if it is to be attached 10 feet from the top and is to make an angle of 35 with the ground Give your answer to the nearest tenth of a s Example A ship is 8 miles west and 24 miles south of a harbor What bearing should the captain set to sail directly to harbor Round to the nearest tenth Example A jet leaves a runway whose bearing is 38 E from the control tower After ying 7 miles the jet turns 90 and ies on a bearing of S 52 E for 8 miles At that time what is the bearing of the jet from the control tower