Find the missing parts of a right triangle Use trig ratios to solve problems

1. 4.11.5 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

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
ED
tan67
6
ED 6tan67
14.1
° =
= °
≈
m D 90 67 23∠ = − = °
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
ED
tan67
6
ED 6tan67
14.1
° =
= °
≈
m D 90 67 23∠ = − = °
2 2 2
BD 6 14.1
BD 234.81
15.3
= +
=
≈
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
TA 18 12
TA 468 21.6
= +
= ≈
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
TA 18 12
TA 468 21.6
= +
= ≈
hyp
opp
adj
1
12
tanT
18
12
T tan
18
34
−
=
 =  
 
≈ °
m A 90 34
56
∠ = −
= °
21.6
56°
34°