Find the missing parts of right triangles

1. Obj. 41 Solving Right Triangles
The student is able to (I can):
• Find the missing parts of a right triangle
• Use trig ratios to solve problems

2. To “solve” a right triangle means to find all
of the missing parts of the right triangle.
If you are given an angle and a side:
• Subtract the angle from 90° to find the
other acute angle
• Use trig ratios to find one of the missing
sides
• Use either trig ratios or Pythagorean
Theorem to find the third side

3. If you are given two sides:
• Use Pythagorean Theorem to find the
missing side
• Use trig ratios to find an angle
— Unless all of your sides work out to
be whole numbers, be sure to use the
two given sides in your trig ratio to
prevent rounding errors.
• Subtract the angle you found from 90°
to find the other angle

4. Examples
Solve the triangles. Round sides to the
nearest tenth and angles to the nearest
whole degree.
E
adj
6
1.
B
67°
m∠D=_____
23°
14.1
ED = ______
BD = ______
15.3
opp
hyp
D
m∠D = 90 − 67 = 23°
ED
tan67° =
6
ED = 6 tan67°
≈ 14.1
BD2 = 6 2 + 14.12
BD = 234.81
≈ 15.3

5. 2. TA = _____
21.6
m∠A = _____
56°
34°
m∠T = _____
A
hyp
12 opp
T
2
2
TA = 18 + 12
2
18
adj
M
TA = 468 ≈ 21.6
It doesn’t matter whether you use ∠T
or ∠A. The triangle is labeled for ∠T.
tanT =
12
18
12 
T = tan−1  

 18 
≈ 34°
m∠A = 90 − 34
= 56°