Basic Mathematics for College Students

750 Chapter 9 An Introduction to Geometry

We must find a number that, when squared, is 32. Since represents the length of a

side of a triangle, we consider only the positive square root.

This is the exact length.

The missing side length is exactly inches long. Since 32 is not a perfect square,

its square root is not a whole number. We can use a calculator to approximate.

To the nearest hundredth, the missing side length is 5.66 inches.

132 in.5.66 in.

132

132

b 132

b

17 in.

a in.

27 in.

Using Your CALCULATOR Finding the Width of a TV Screen

The size of a television screen is the diagonal

measure of its rectangular screen. To find the

length of a 27-inch screen that is 17 inches

high, we use the Pythagorean theorem

with and.

Since the variable represents the length of

the television screen, it must be positive. To find ,

we find the positive square root of the result when 17^2 is subtracted from 27^2.

Using a radical symbol to indicate this, we have

We can evaluate the expression on the left side by entering:

27 17

To the nearest inch, the length of the television screen is 21 inches.

( x^2  x^2 ) 1 20.97617696

2272  172 a

a

a

272  172 a^2

272 a^2  172

c^2 a^2 b^2

c 27 b 17

3 Use the converse of the Pythagorean theorem.

If a mathematical statement is written in the form if p ...,then q.. ., we call the

statement if q ...,then p.. .its converse.The converses of some statements are true,

while the converses of other statements are false. It is interesting to note that the

converse of the Pythagorean theorem is true.

Converse of the Pythagorean Theorem

If a triangle has three sides of lengths ,,and ,such that , then

the triangle is a right triangle.

ab c a^2 b^2 c^2

EXAMPLE (^5) Is the triangle shown here a right
triangle?
StrategyWe will substitute the side lengths, 6, 8, and
11, into the Pythagorean equation.
WHYBy the converse of the Pythagorean theorem, the
triangle is a right triangle if a true statement results. The triangle is not a right
triangle if a false statement results.
a^2 b^2 c^2
6 m
8 m
11 m
Self Check 5
Is the triangle below a right
triangle?
48 ft
73 ft 55 ft