GEOMETRY

The length of the hypotenuse is 10 3.

h = 2 • 5 6 hypotenuse = 2 • leg

h = 5 12 Simplify.

h = 5 4(3)

h = 5(2) 3

h = 10 3

Use the 45°-45°-90° Triangle Theorem to find the hypotenuse.

Special Right TrianglesLESSON 8-2

Additional Examples

Find the length of the hypotenuse of a 45°-45°-90°

triangle with legs of length 5 6.

GEOMETRY

22 2x = • Simplify by rationalizing the

denominator.

2 2

22 2

x = Divide each side by 2.

Use the 45°-45°-90° Triangle Theorem to find the leg.

x = 11 2 Simplify.

22 = 2 • leg hypotenuse = 2 • leg

The length of the leg is 11 2.

22 2 2x =

Find the length of a leg of a 45°-45°-90° triangle with a

hypotenuse of length 22.

Special Right TrianglesLESSON 8-2

Additional Examples

GEOMETRY

The distance from one corner to the opposite corner, 96 ft, is the length of the hypotenuse of a 45°-45°-90° triangle.

Each side of the playground is about 68 ft.

96 = 2 • leg hypotenuse = 2 • leg

leg = Divide each side by 2. 96 2

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?

Special Right TrianglesLESSON 8-2

Additional Examples

leg = Use a calculator.

GEOMETRY

The length of the shorter leg is 6 3, and the length of the hypotenuse is 12 3.

d = 6 3 Simplify.

f = 2 • 6 3 hypotenuse = 2 • shorter leg

f = 12 3 Simplify.

The longer leg of a 30°-60°-90° triangle has length 18. Find the lengths of the shorter leg and the hypotenuse.

18 = 3 • shorter leg longer leg = 3 • shorter leg

d = Divide each side by 3. 18 3

d = • Simplify by rationalizing

the denominator.

3 3

18 3

18 3 3

d =

You can use the 30°-60°-90° Triangle Theorem to find the lengths.

Special Right TrianglesLESSON 8-2

Additional Examples

GEOMETRY

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.

Special Right TrianglesLESSON 8-2

Additional Examples

GEOMETRY

h = 12.5 3 longer leg = 3 • shorter leg

(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 = = 12.5 Divide each side by 2.25 2

Special Right TrianglesLESSON 8-2

Additional Examples

h ≈ 21.65

The perpendicular height between the two bases is about 21.7 ft.