1. Use the Pythagorean Theorem to find the unknown side of the right triangle. Simplify your answer. Write an exact answer, using radicals as needed.
2. Find the length of the third side of the right triangle. Round to the nearest thousandth.
3. You are going to use an inclined plane to lift a heavy object to the top of a shelving unit with a height of 6 ft. The base of the inclined plane is 16 ft from the shelving unit. What is the length of the inclined plane? Round to the nearest tenth as needed.
4. What is the slant height of the pyramid? Round to the nearest tenth as needed.
5. Writing Find the length of the hypotenuse of the right triangle. Explain how you can interpret the Pythagorean Theorem using the areas of squares.
6. Reasoning You are painting the roof of a shed that is 35 ft from the ground. You are going to place the base of a ladder 12 ft from the shed.
a. How long does the ladder need to be to reach the roof of the shed? Simplify your answer.
b. Explain how shortening the distance between the ladder and the shed affects the height of the ladder.
7. Error Analysis A student was asked to find the slant height of a square pyramid if the length of each side of the base is 24 cm and the height is 25 cm. She incorrectly said the slant height is 7 cm.
a. Find the slant height of the pyramid. Round to the nearest tenth as needed.
b. What mistake might the student have made?
8. Pyramid Dimensions Each face of the pyramid is a triangle with the dimensions shown. How far is a corner of the base from the top of the pyramid? Round to the nearest tenth as needed.