Download 9.4 Special Right Triangles

9.4 Special Right Triangles
45-45-90
30-60-90
Exceedingly Essential for Pre-Cal
Theorem
In a Right triangle, if the acute angles are 45
degrees, then the legs are equal and the
hypotenuse equals the length of the leg
times square root of two.
Solve for x
45
5
x
Solve for x
45
5
x 5
2
5
Solve for a
a
a
45
45
12
Solve for a
12  a 2
12
a
2
a
a
12 2
6 2a
2
45
45
12
Theorem
In a Right triangle, if the acute angles are
thirty degree and sixty degree, then the side
across the hypotenuse is twice the side
across from the thirty degree angle. The side
across from the sixty degree equals the sides
across from the thirty degree angle times
square root of three.
Solve for x and r
60
r
8
30
x
Solve for x and r
60
r  16
8
30
x  8 3
Find r and x
30
r
18
60
x
Find r and x
30
r
18
60
x
18  x  3
18 18 3

6 3 x
3
3
Find r and x
30
18
r  12 3
60
x 6 3
Burn into your memory
the 30-60-90
and 45-45-90 triangles.
When you do the Unit
Circle, you will need it
Homework
Page 554 – 555
# 12 - 26
Homework
Page 554 – 555
# 27 - 34, 37,
38, 42, 47 - 49