Assignment: Use the Pythagorean Theorem
Choose any three (3) of the following five problems to solve. Be sure to show all work leading to
your answer.
1. A car drives 12 miles north, turns, and then drives 8 miles east. How far is the car from its
starting point?
a. Draw a right triangle to represent this situation. Label the lengths of the known sides.
Label the length of the unknown side x.
b. Use the Pythagorean theorem to find the length of the missing side. Be sure to
indicate which root represents the answer and write the answer in simplest radical
form.
12^2 + 8^2 = x^2
144 + 64 = x^2
208 = x^2
√208 = √x^2
√4
52 = a√x^2
c. * Use
calculator to change the answer to decimal form. Round the answer to the
2√52nearest
=x
tenth. Using this decimal number, write a sentence to explain the meaning of
the answer in this situation.
2√52 ≈ 14.4
In this situation, the number 14.4 means that the car is now about 14.4 miles from its
starting point.
2. A firefighter in training leans a 21-foot extension ladder against an office building. How far
from the building should the ladder be placed if the firefighter wants to reach a window
that is 15 feet above the ground?
a. Draw a right triangle to represent this situation. Label the lengths of the known sides.
Label the length of the unknown side x.
b. Use the Pythagorean theorem to find the length of the missing side. Be sure to
indicate which root represents the answer and write the answer in simplest radical
form.
x^2 + 15^2 = 21^2
x^2 + 225 = 441
x^2 + 225 - 225 = 441 - 225
x^2 = 216
√x^2 = √216
√x^2 = √4 * 54
x = 2√54
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c.
Use a calculator to change the answer to decimal form. Round the answer to the
nearest tenth. Using this decimal number, write a sentence to explain the meaning of
the answer in this situation.
2√54 ≈ 14.7
In this situation, the number 14.7 means that the ladder should be placed about 14.7 feet
away from the building.
3. The size of flat-screen TVs are usually based on the diagonal measurement across the
screen. If a flat-screen TV has a height of 26 inches and a width of 40 inches, what is the
diagonal measurement of the TV?
a. Draw a right triangle to represent this situation. Label the lengths of the known sides.
Label the length of the unknown side x.
b. Use the Pythagorean theorem to find the length of the missing side. Be sure to
indicate which root represents the answer and write the answer in simplest radical
form.
40^2 + 26^2 = x^2
1600 + 676 = x^2
2276 = x^2
√2276 = √x^2
√4 *Use
569 =
c.
a √x^2
calculator to change the answer to decimal form. Round the answer to the
2√569
= x tenth. Using this decimal number, write a sentence to explain the meaning of
nearest
the answer in this situation.
2√569 ≈ 47.7
In this situation, the number 47.7 means that the diagonal measurement of the TV is
about 47.7 inches.
4. Aaron was standing directly across the river from his friend at a distance of 10 feet away.
While his friend stood still, Aaron walked a straight line along the river’s edge , ending up
16 feet away. How far did Aaron walk?
a. Draw a right triangle to represent this situation. Label the lengths of the known sides.
Label the length of the unknown side x.
b. Use the Pythagorean theorem to find the length of the missing side. Be sure to
indicate which root represents the answer and write the answer in simplest radical
form.
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c.
Use a calculator to change the answer to decimal form. Round the answer to the
nearest tenth. Using this decimal number, write a sentence to explain the meaning of
the answer in this situation.
5. A construction worker plans to build a diagonal walking path through a rectangular park.
If the dimensions of the park are 10 yards × 14 yards, what will the length of the path be?
a. Draw a right triangle to represent this situation. Label the lengths of the known sides.
Label the length of the unknown side x.
b. Use the Pythagorean theorem to find the length of the missing side. Be sure to
indicate which root represents the answer and write the answer in simplest radical
form.
c.
Use a calculator to change the answer to decimal form. Round the answer to the
nearest tenth. Using this decimal number, write a sentence to explain the meaning of
the answer in this situation.
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