Warm Up
Find the value of x. Leave your answer in simplest radical form.
7 x
9
x
7
9
7.3: Special Right Triangles
Objectives:To use the properties of 45-45-90 and 30-60-90 right triangles
45°-45°-90° Right TriangleIt is an isosceles, right triangle– Both legs are congruent!!
THEOREM:The hypotenuse is times the length of the legs2
IF YOU NEED TO FIND THE HYPOTENUSE: Hypotenuse = (Length of Leg) X
IF YOU NEED TO FIND A LEG:
Length of leg =
2
2
Hypotenuse
Examples:
1. Find h: 2. Find x:
9
h
22
x
Find x:
35x
Find x:
1. 2.
6
x
23x
Find x:
10
x
A square has a perimeter of 24 inches. How long is the diagonal?
30°-60°-90° Right Triangle Shorter Leg is the side opposite the 30° angle Longer leg is the side opposite the 60° angle
Let the shorter leg = nHYPOTENUSE = 2 SHORTER LEG∙
= 2n
LONGER LEG = SHORTER LEG = n
33
If you need to find the shorter leg (side opposite 30°):
If given the hypotenuse:
SHORTER LEG =
If given the longer leg:
SHORTER LEG=
2
Hypotenuse
3
LongerLeg
Fill in the table of values for the side lengths of a 30-60-90 triangle:
Shorter Leg Longer Leg Hypotenuse
3
4
15
34
10
35
32
28
Find the missing lengths.
1. 2. 60
30
g
f
5
xy
6
Find the variables.
1. 2.
30
60
4
x
y
60
30
52
k
m
Find the value of each variable.(Figure not drawn to scale)
b
cd
a
4530
27
Find the value of each variable. Leave your answer in simplest radical form.
23
b
a
4
45°
Find the area. Round your answer to the nearest tenth.
60 60
cm38
Find the area of the triangle.
45
.214 in
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