Chapter 8: Right Triangles & Trigonometry

8.2

Special Right Triangles

Isosceles Right Triangles

• What are the angle measures of an isosceles right triangle?

Theorem 8-5

• 45-45-90 Triangle Theorem– In a 45-45-90 triangle, both legs are congruent and

the length of the hypotenuse is √2 times the length of a leg

s 2 s

s

Example 1

• Find the value of h:

h

9

45 45

Example 1

• Find the value of x:

2 2x

45

45

Example 1a

• Find the length of the hypotenuse of a 45-45-90 triangle with legs of length 5√3.

Example 2

• What is the value of x?

x6

Example 3• A high school softball diamond is a square.

The distance from base to base is 60 feet. To the nearest foot, how far does a catcher throw the ball from home plate to second base?

Example 3a

• A square garden has sides 100 ft long. You want to build a brick path along a diagonal of the square. How long will the path be?

Theorem 8-6

• 30-60-90 Triangle Theorem– In a 30-60-90 triangle, the length of the hypotenuse

is twice the length of the shorter leg. The length of the longer leg is √3 times the length of the shorter leg.

x 3

x

2x

60

30

Example 4

• Find the value of each variable:

60 30

5

f

d

Example 4a• Find the value of each variable:

y

x8

60

30

Homework

• p. 428

• 1-6, 9-14, 17-22