You have 1000 feet of flexible pool siding and wish to construct a swimming pool

A(n) triangle is one that contains an angle of 90 degrees.The longest side is called the .

For a triangle with base b and altitude h, a formula for the area A is .

The formula for the circumference C of a circle of radius r is.

Two triangles are if corresponding angles are equal and the lengths of the corresponding sides are proportional.

True or False In a right triangle, the square of the length of the longest side equals the sum of the squares of the lengths of the other two sides.

True or False The triangle with sides of length 6, 8, and 10 is a right triangle.

True or False The volume of a sphere of radius r is

True or False The triangles shown are congruent.

True or False The triangles shown are similar.

True or False The triangles shown are similar.

In Problems 1116, the lengths of the legs of a right triangle are given. Find the hypotenuse a = 5, b = 12

In Problems 1116, the lengths of the legs of a right triangle are given. Find the hypotenuse a = 6, b = 8

In Problems 1116, the lengths of the legs of a right triangle are given. Find the hypotenuse a = 10, b = 24

In Problems 1116, the lengths of the legs of a right triangle are given. Find the hypotenuse a = 4, b = 3

In Problems 1116, the lengths of the legs of a right triangle are given. Find the hypotenuse a = 7, b = 24

In Problems 1116, the lengths of the legs of a right triangle are given. Find the hypotenuse a = 14, b = 48

In Problems 1724, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse 3, 4, 5

In Problems 1724, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse 6, 8, 10

In Problems 1724, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse 4, 5, 6

In Problems 1724, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse 2, 2, 3

In Problems 1724, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse 7, 24, 25

In Problems 1724, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse 10, 24, 26

In Problems 1724, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse 6, 4, 3

In Problems 1724, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse 5, 4, 7

Find the area A of a rectangle with length 4 inches and width 2 inches.

Find the area A of a rectangle with length 9 centimeters and width 4 centimeters.

Find the area A of a triangle with height 4 inches and base 2 inches.

Find the area A of a triangle with height 9 centimeters and base 4 centimeters.

Find the area A and circumference C of a circle of radius 5 meters.

Find the area A and circumference C of a circle of radius 2 feet.

Find the volume V and surface area S of a rectangular box with length 8 feet, width 4 feet, and height 7 feet.

Find the volume V and surface area S of a rectangular box with length 9 inches, width 4 inches, and height 8 inches.

Find the volume V and surface area S of a sphere of radius 4 centimeters.

Find the volume V and surface area S of a sphere of radius 3 feet.

Find the volume V and surface area S of a right circular cylinder with radius 9 inches and height 8 inches.

Find the volume V and surface area S of a right circular cylinder with radius 8 inches and height 9 inches.

In Problems 3740, find the area of the shaded region

In Problems 3740, find the area of the shaded region

In Problems 3740, find the area of the shaded region

In Problems 3740, find the area of the shaded region

In Problems 4144, each pair of triangles is similar. Find the missing length x and the missing angles A, B, and C.

In Problems 4144, each pair of triangles is similar. Find the missing length x and the missing angles A, B, and C.

In Problems 4144, each pair of triangles is similar. Find the missing length x and the missing angles A, B, and C.

In Problems 4144, each pair of triangles is similar. Find the missing length x and the missing angles A, B, and C.

How many feet does a wheel with a diameter of 16 inches travel after four revolutions?

How many revolutions will a circular disk with a diameter of 4 feet have completed after it has rolled 20 feet?

In the figure shown, is a square, with each side of length 6 feet. The width of the border (shaded portion) between the outer square and is 2 feet. Find the area of the border.

Refer to the figure. Square has an area of 100 square feet; square has an area of 16 square feet.What is the area of the triangle CGF ?

Architecture A Norman window consists of a rectangle surmounted by a semicircle. Find the area of the Norman window shown in the illustration. How much wood frame is needed to enclose the window?

Construction A circular swimming pool, 20 feet in diameter, is enclosed by a wooden deck that is 3 feet wide. What is the area of the deck? How much fence is required to enclose the deck?

How Tall Is the Great Pyramid? The ancient Greek philosopher Thales of Miletus is reported on one occasion to have visited Egypt and calculated the height of the Great Pyramid of Cheops by means of shadow reckoning. Thales knew that each side of the base of the pyramid was 252 paces and that his own height was 2 paces. He measured the length of the pyramids shadow to be 114 paces and determined the length of his shadow to be 3 paces. See the illustration. Using similar triangles, determine the height of the Great Pyramid in terms of the number of paces.

The Bermuda Triangle Karen is doing research on the Bermuda Triangle which she defines roughly by Hamilton, Bermuda; San Juan, Puerto Rico; and Fort Lauderdale, Florida. On her atlas Karen measures the straight-line distances from Hamilton to Fort Lauderdale, Fort Lauderdale to San Juan, and San Juan to Hamilton to be approximately 57 millimeters (mm), 58 mm, and 53.5 mm respectively. If the actual distance from Fort Lauderdale to San Juan is 1046 miles, approximate the actual distances from San Juan to Hamilton and from Hamilton to Fort Lauderdale. Source: Reprinted with permission from Red River Press, Inc., Winnipeg, Canada.

In Problems 5355, use the facts that the radius of Earth is 3960 miles and 1 mile = 5280 feet How Far Can You See? The conning tower of the U.S.S. Silversides, a World War II submarine now permanently stationed in Muskegon, Michigan, is approximately 20 feet above sea level. How far can you see from the conning tower?

In Problems 5355, use the facts that the radius of Earth is 3960 miles and 1 mile = 5280 feet How Far Can You See? A person who is 6 feet tall is standing on the beach in Fort Lauderdale, Florida, and looks out onto the Atlantic Ocean. Suddenly, a ship appears on the horizon. How far is the ship from shore?

In Problems 5355, use the facts that the radius of Earth is 3960 miles and 1 mile = 5280 feet How Far Can You See? The deck of a destroyer is 100 feet above sea level. How far can a person see from the deck? How far can a person see from the bridge, which is 150 feet above sea level?

Suppose that m and n are positive integers with If and show that a, b, and c are the lengths of the sides of a right triangle. (This formula can be used to find the sides of a right triangle that are integers, such as 3, 4, 5; 5, 12, 13; and so on. Such triplets of integers are called Pythagorean triples.)

You have 1000 feet of flexible pool siding and wish to construct a swimming pool. Experiment with rectangularshaped pools with perimeters of 1000 feet. How do their areas vary? What is the shape of the rectangle with the largest area? Now compute the area enclosed by a circular pool with a perimeter (circumference) of 1000 feet. What would be your choice of shape for the pool? If rectangular, what is your preference for dimensions? Justify your choice. If your only consideration is to have a pool that encloses the most area, what shape should you use?

The Gibbs Hill Lighthouse, Southampton, Bermuda, in operation since 1846, stands 117 feet high on a hill 245 feet high, so its beam of light is 362 feet above sea level. A brochure states that the light itself can be seen on the horizon about 26 miles distant. Verify the correctness of this information. The brochure further states that ships 40 miles away can see the light and planes flying at 10,000 feet can see it 120 miles away. Verify the accuracy of these statements. What assumption did the brochure make about the height of the ship?