The length of the hypotenuse is 10 3.
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Transcript of The length of the hypotenuse is 10 3.
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.