Transcript Two Special Right Triangle

7.4: Special Right Triangles
Objectives:
1. To use the properties of 45-45-90 and
30-60-90 right triangles to solve problems
Special Right Triangle Theorem
45°-45°-90° Triangle
Theorem
In a 45°-45°-90°
triangle, the
hypotenuse is 2
times as long as
each leg.
hypotenuse  leg  2
Example 2
A fence around a square garden has a
perimeter of 48 feet. Find the approximate
length of the diagonal of this square
garden.
FoxTrot
Special Right Triangle Theorem
30°-60°-90° Triangle
Theorem
In a 30°-60°-90°
triangle, the
hypotenuse is twice
as long as the shorter
hypotenuse  2  shorter leg
leg, and the longer
longer leg  shorter leg  3
leg is 3 times as long
as the shorter leg.
Two Special Right Triangles
Example 3
Find the value of each variable. Write your
answer in simplest radical form.
1.
2.
3.
X=4
X=13
Y=4√3
Y=26
Y=12
X=12√2
Example 4
Find the value of each variable. Write your
answer in simplest radical form.
1.
X=Y=7
√2
7 x√2 = 7√2
√2 √2
2
2.
3.
Example 6: SAT
In the figure, what is the ratio of RW to WS?
2X
√3
T
=2
X
X
√3
2X
√3
60
30
S
W
R
2X
√3
X
√3