4-1: TEKS Practice

  • 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.

    A right triangle with legs of length 10 and 24 and a hypotenuse of unknown length.

  • 2. Find the length of the third side of the right triangle. Round to the nearest thousandth.

    A right triangle with legs of length 7 in. and 16 in. and a hypotenuse of length c in.

  • 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.

    A right triangle with legs of length 16 ft and 6 ft and a hypotenuse of unknown length. The 16 ft leg is horizontal, and a box rests on the hypotenuse.

  • 4. What is the slant height of the pyramid? Round to the nearest tenth as needed.

    The slant height of a square pyramid forming the hypotenuse of a right triangle with vertical and horizontal legs of length 25 m and 14 m.

  • 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.

    A right triangle with legs of length 32 and 60 and a hypotenuse of length c.

  • 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 ladder forming the hypotenuse of a right triangle with vertical and horizontal legs of length 35 ft and 12 ft.

    • 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.

    A square pyramid with slant height 606 ft and half base side length 367 ft.


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Table of Contents

Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties