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Similar Figure and Pythagorean Theorem Word Problems Practice Questions (page 2)

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Updated on Oct 3, 2011

Practice 2

Use the Pythagorean theorem and the word-problem solving steps to solve the word problems in the following practice set.

Problems

  1. A wire attached to a 16-ft. pole is anchored into the ground 12 ft. from the base of the pole. How long is the wire?
  2. A person is flying a kite. The string attached to the kite is 17 m long. If the kite is exactly 15 m horizontally from the person, how high is the kite off the ground?
  3. A flagpole is 12 ft. tall. A person raising the flag is holding a rope attached to the top of the pole. If the rope is 15 ft. long, how many feet is the person from the base of the pole?

Solutions

  1. Read and understand the question. This question is looking for the length of the wire when the height of the pole and the distance from the base are known. The length of the wire is the hypotenuse of a right triangle.
  2. Make a plan. Use the strategy of drawing a picture. Then, use the formula a2+ b2= c2and substitute the given values. Finally, solve the equation for the unknown value.

    Carry out the plan. Draw a picture of the pole and the wire, as shown in the following figure.

    similar figure and Pythagorean theorem word problems_Answers

    The legs are 16 ft. and 12 ft., so a = 16 and b = 12. Use the formula a2+ b2= c2and substitute the given values.

      162+ 122= c2

    Evaluate the exponents.

      256 + 144 = c2

    Add.

      400 = c2

    Take the positive square root of each side of the equation.

      20 = c

    The length of the wire is 20 ft.

    Check your answer. To check this answer, substitute the lengths of the three sides into the formula. The formula a2+ b2= c2becomes 162+ 122= 202.

    Apply the exponents to get 256 + 144 = 400. Add the numbers on the left side to get 400 = 400. This answer is checking.

  3. Read and understand the question. This question is looking for the height of a kite a person is flying. The length of the kite string and the horizontal distance from the person to the kite are known.
  4. Make a plan. Use the strategy of drawing a picture. Then, use the formula a2+ b2= c2and substitute the given values. Finally, solve the equation for the unknown value.

    Carry out the plan. Draw a picture of the person flying the kite, as shown in the following figure.

    similar figure and Pythagorean theorem word problems_Answers

    One leg is 15 m and the hypotenuse is 17 m, so a = 15 and c = 17. Use the formula a2+ b2= c2and substitute the given values.

      152+ b2= 172

    Evaluate the exponents.

      225 + b2= 289

    Subtract 225 from each side of the equation to get the variable alone.

      225 – 225 + b2= 289 – 225
      b2= 64

    Take the positive square root of each side of the equation: b = 8. The length of the other leg is 8, so the height of the kite is 8 m.

    Check your answer. To check this answer, substitute the lengths of the three sides into the formula. The formula a2+ b2= c2becomes 152+ 82= 172.

    Apply the exponents to get 225 + 64 = 289. Add the numbers on the left side to get 289 = 289. This answer is checking.

  5. Read and understand the question. This question is looking for the distance a person is from a flagpole. The height of the pole and the length of a rope attached to the top of the pole are known.
  6. Make a plan. Use the strategy of drawing a picture. Then, use the formula a2+ b2= c2and substitute the given values. Finally, solve the equation for the unknown value.

    Carry out the plan. Draw a picture of the flagpole and the person holding the rope, as shown in the following figure.

    similar figure and Pythagorean theorem word problems_Answers

    One leg is 12 ft. and the hypotenuse is 15 ft., so a = 12 and c = 15. Use the formula a2+ b2= c2and substitute the given values.

      122+ b2= 152

    Evaluate the exponents.

      144 + b2= 225

    Subtract 144 from each side of the equation to get the variable alone.

      144 – 144 + b2= 225 – 144
      b2= 81

    Take the positive square root of each side of the equation: b = 9. The length of the other leg is 9, so the person is 9 feet from the base of the pole.

    Check your answer. To check this answer, substitute the lengths of the three sides into the formula. The formula a2+ b2= c2becomes 122+ 92= 152.

    Apply the exponents to get 144 + 81= 225. Add the numbers on the left side to get 225 = 225. This answer is checking.

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