13.5 Special Right Triangles
Date: ________
What kind of triangle is this?
45
Can we find the length of the
hypotenuse?
45
Isosceles Right Triangle Theorem
In an isosceles right triangle, if a leg is x, then the hypotenuse is x
What kind of triangle is this?
60
30 -60 -90 Triangle Theorem
60
60
Can we find its altitude
In a 30­60­90 triangle, if the shorter leg is x then the longer leg is x√3 and the hypotenuse is 2x
Examples:
1.
What are the lengths of the legs of a 30°-60°-90° right triangle whose
hypotenuse has a length of 50?
2.
An airport is to be built on a piece of land 2 mile square. Approximate the
length of the longest runway that the airport can have.
3.
Approximate the lengths of the legs of an isosceles right triangle whose
hypotenuse has a length of 10.
4.
ΔABC is an isosceles right triangle and m<DAC=30°. If AC = 4, what is the
length of BD?
B
D
A
5.
In ΔXYZ, m<Z = 45º, m<Y = 30º, and XY = 8. Find XZ and YZ.
X
8
h
Z
45
30
W
Y
C