7.4: Special Right Triangles

Objectives:

1. To use the properties of 45-45-90 and 30-60-90 right triangles to solve problems

Special Right Triangle Theorem45°-45°-90° Triangle

Theorem

In a 45°-45°-90° triangle, the hypotenuse is times as long as each leg.

2

2leg hypotenuse

Example 2

A fence around a square garden has a perimeter of 48 feet. Find the approximate length of the diagonal of this square garden.

FoxTrot

Special Right Triangle Theorem30°-60°-90° Triangle

Theorem

In a 30°-60°-90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg.

3

legshorter 2 hypotenuse 3legshorter leglonger

Two Special Right Triangles

Example 3

Find the value of each variable. Write your answer in simplest radical form.

1. 2. 3.

X=4

Y=4

X=13

Y=26 Y=12

X=12

Example 4

Find the value of each variable. Write your answer in simplest radical form.

1. 2. 3.

X=Y=7 2 7 x2 = 72 2 2

Example 6: SAT

In the figure, what is the ratio of RW to WS?

6030

WR

T

S

X

X

2 X

2 X

2 X

X= 2