1. Use the 45°-45°-90° Triangle Theorem to find the hypotenuse.
May 9, 2003
Special Right Triangles
LESSON 8-2
Additional Examples
Find the length of the hypotenuse of a 45°-45°-90° triangle with legs of length
Use the 45°-45°-90° Triangle Theorem to find the hypotenuse.
h = • hypotenuse = 2 • leg
h = Simplify.
h = (3)
h = 5(2) 3
h =
The length of the hypotenuse is
Quick Check

2. Use the 45°-45°-90° Triangle Theorem to find the leg.
May 9, 2003
Special Right Triangles
LESSON 8-2
Additional Examples
Find the length of a leg of a 45°-45°-90° triangle with a hypotenuse of length 22.
Use the 45°-45°-90° Triangle Theorem to find the leg.
22 = 2 • leg hypotenuse = • leg 22 2
x = Divide each side by 22 2
x = • Simplify by rationalizing the
denominator. 2
x =
x = Simplify.
The length of the leg is
Quick Check

3. of the hypotenuse of a 45°-45°-90° triangle.
May 9, 2003
Special Right Triangles
LESSON 8-2
Additional Examples
The distance from one corner to the opposite corner of a square playground is 96 ft. To the nearest foot, how long is each side of the playground?
The distance from one corner to the opposite corner, 96 ft, is the length
of the hypotenuse of a 45°-45°-90° triangle.
96 = • leg hypotenuse = • leg
leg = Divide each side by 2. 96 2
leg = Use a calculator.
Each side of the playground is about 68 ft.
Quick Check

4. The longer leg of a 30°-60°-90° triangle has
May 9, 2003
Special Right Triangles
LESSON 8-2
Additional Examples
Quick Check
The longer leg of a 30°-60°-90° triangle has
length 18. Find the lengths of the shorter leg and the hypotenuse.
You can use the 30°-60°-90° Triangle Theorem to find the lengths.
18 = 3 • shorter leg longer leg = • shorter leg
d = Divide each side by 3. 18 3
d = • Simplify by rationalizing
the denominator. 3 18 3
d =
d = Simplify.
f = 2 • hypotenuse = 2 • shorter leg
f = Simplify.
The length of the shorter leg is , and the length of the hypotenuse is

5. A garden shaped like a rhombus has a perimeter of 100 ft
May 9, 2003
Special Right Triangles
LESSON 8-2
Additional Examples
A garden shaped like a rhombus has a perimeter of 100 ft
and a 60° angle. Find the perpendicular height between the two
bases.
Because a rhombus has four sides of equal length, each side is 25 ft.
Draw the rhombus with altitude h,
and then solve for h.

6. you can use the properties of 30°-60°-90° triangles.
May 9, 2003
Special Right Triangles
LESSON 8-2
Additional Examples
(continued)
The height h is the longer leg of the right triangle. To find the height h,
you can use the properties of 30°-60°-90° triangles.
25 = 2 • shorter leg hypotenuse = 2 • shorter leg
shorter leg = = Divide each side by 2. 25 2
h = longer leg = 3 • shorter leg
h ≈
The perpendicular height between the two bases is about 21.7 ft.
Quick Check