1. Special Right Triangles
Lesson 6-3
Special Right Triangles

2. 30°- 60°- 90° Triangle
The sides of a triangle whose angles measure 30°, 60° and 90° have a special relationship. The hypotenuse is always twice as long as the side opposite the 30° angle.
c = 2a or a = ½ c
60°
30° a b c
Side opposite 30° angle.

3. Find each missing length.
Find the length of side c. Then find the length of side b.
30°
60° b c
6 in
a2 + b2 = c2
b2 = c2 – a2
b2 = 122 – 62
b2 = 144 – 36
b2 = 108
b ≈ 10.4 in
C = 2a
C = 2(6 in)
C = 12 in

4. Find the length of side a. Then find the length of side b.
60°
30°
15 cm a b
a2 + b2 = c2
b2 = c2 – a2
b2 = 152 – 7.52
b2 = 225– 56.25
b2 =
b ≈ 13 cm
a = ½c
a = ½ (15 cm)
a = 7.5 cm

5. 45°-45° Right Triangle c a 45° b
Sides a and b are equal. Use Pythagorean to find the missing side.
a2 + b2 = c2

6. Find each missing length.
45°
9 m b c
If a = 9, then b = 9
= c2
162 = c2
12.7 m ≈ c

7. 45° c b
18 yd
If a = 18, then b = 18
= c2
648= c2
25.5 yd ≈ c