Transcript Special Right Triangles LESSON 8-2 Additional Examples Find the length of the hypotenuse of a 45°-45°-90° triangle with legs of length 5 6. Use the.

Special Right Triangles
LESSON 8-2
Additional Examples
Find the length of the hypotenuse of a 45°-45°-90°
triangle with legs of length 5 6.
Use the 45°-45°-90° Triangle Theorem to find the hypotenuse.
h=
2•5
h=5
12
h=5
4(3)
h = 5(2)
h = 10
6
hypotenuse =
2 • leg
Simplify.
3
3
The length of the hypotenuse is 10
3.
Quick Check
HELP
GEOMETRY
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
x = 22
x=
22
•
2
22
2
2
2.
Simplify by rationalizing the
denominator.
2
2
x = 11
2
The length of the leg is 11
HELP
2 • leg
Divide each side by
2
x=
hypotenuse =
Simplify.
2.
Quick Check
GEOMETRY
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 =
leg =
2 • leg
96
2
hypotenuse =
2 • leg
Divide each side by
2.
Use a calculator.
Each side of the playground is about 68 ft.
Quick Check
HELP
GEOMETRY
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 =
d=
18
3
Divide each side by
d=
18 •
3
d = 18
3
3
3 • shorter leg
3.
Simplify by rationalizing
the denominator.
3
3
d=6
3
f=2•6
Simplify.
3
hypotenuse = 2 • shorter leg
f = 12 3
Simplify.
The length of the shorter leg is 6 3, and the length of the hypotenuse is 12
HELP
GEOMETRY
3.
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.
HELP
GEOMETRY
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
25
shorter leg = 2 = 12.5
h = 12.5
3
hypotenuse = 2 • shorter leg
Divide each side by 2.
longer leg =
3 • shorter leg
h ≈ 21.65
The perpendicular height between the two bases is about 21.7 ft.
Quick Check
HELP
GEOMETRY