Use trigonometry and the Pythagorean Theorem to find all of the missing sides and angles of a right triangle.

1. 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.
1. m∠D=_____
ED = ______
BD = ______
6
67°B
E
D
tan67
6
6tan67
14.1
ED
ED
° =
= °
≈
m 90 67 23D∠ = − = °

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

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

7. 2. TA = _____
m∠A = _____
m∠T = _____
12
18
T
A
M

8. 2. TA = _____
m∠A = _____
m∠T = _____
It doesn’t matter whether you use ∠T or ∠A. The
triangle is labeled for ∠T.
12
18
T
A
M2 2 2
18 12
468 21.6
TA
TA
= +
= ≈
hyp
opp
adj
21.6

9. 2. TA = _____
m∠A = _____
m∠T = _____
It doesn’t matter whether you use ∠T or ∠A. The
triangle is labeled for ∠T.
12
18
T
A
M2 2 2
18 12
468 21.6
TA
TA
= +
= ≈
hyp
opp
adj
1
12
tan
18
12
tan
18
34
T
T −
=
 
=  
 
≈ °
90 34
56
m A∠ = −
= °
21.6
56°
34°