Page 356 - Basic College Mathematics with Early Integers

S E C T I O N 4.6 I SQUARE ROOTS AND THE PYTHAGOREAN THEOREM 333

Objective Using the Pythagorean Theorem

One important application of square roots has to do with right triangles. Recall that a
right triangle is a triangle in which one of the angles is a right angle, or measures
90° (degrees). The hypotenuse of a right triangle is the side opposite the right angle.
The legs of a right triangle are the other two sides. These are shown in the following
figure. The right angle in the triangle is indicated by the small square drawn in
that angle.
The following theorem is true for all right triangles:

Pythagorean Theorem
In any right triangle,
2 2 2
1leg2 + 1other leg2 = 1hypotenuse2

hypotenuse
leg

leg

Using the Pythagorean theorem, we can use one of the following formulas to
find an unknown length of a right triangle:

Finding an Unknown Length of a Right Triangle

2 2
hypotenuse = 21leg2 + 1other leg2
or
2 2
leg = 21hypotenuse2 - 1other leg2

Example 6 Find the length of the hypotenuse of the given right triangle. PRACTICE 6
Find the length of the
hypotenuse of the given right
triangle.
6 ft

8 ft 12 ft
Solution: Since we are finding the hypotenuse, we use the formula
16 ft
2 2
hypotenuse = 21leg2 + 1other leg2
Putting the known values into the formula, we have
2 2
hypotenuse = 2162 + 182 The legs are 6 feet and 8 feet.
= 236 + 64

= 2100
= 10
The hypotenuse is 10 feet long.

Work Practice 6
Answer
6. 20 ft