1. 7.7– Solve Right Triangles

2. Inverse Trig Ratios:
To find the measure of an angle, take the inverse of the trig function. A
7 . 10
sin A° = C B
sin A° = 0.7 BC AB =
mA°
sin
sin
sin-1 AC AB =
mA°
cos-1
A° = sin-1 (0.7)
A° = 44.4° BC AC =
mA°
tan-1

3. 30 tan A° = 20 tan A° = 1.5 A° = tan-1 (1.5) A° = 56.3° O A
1. Use a calculator to approximate the measure of A to the nearest tenth of a degree. 30 20
tan A° =
tan A° = 1.5
A° = tan-1 (1.5)
A° = 56.3° O A
SOH – CAH – TOA

4. 14 sin A° = 26 sin A° = 0.5385 A° = sin-1 (0.53) A° = 32.6° O H
1. Use a calculator to approximate the measure of A to the nearest tenth of a degree. 14 26
sin A° =
sin A° =
A° = sin-1 (0.53)
A° = 32.6° O H
SOH – CAH – TOA

5. 10 cos A° = 16 cos A° = 0.625 A° = cos-1 (0.625) A° = 51.3° A H
1. Use a calculator to approximate the measure of A to the nearest tenth of a degree. 10 16
cos A° =
cos A° = 0.625
A° = cos-1 (0.625)
A° = 51.3° A H
SOH – CAH – TOA

6. O H SOH – CAH – TOA P PQ QR x . 22 c2 = a2 + b2 sin 37° =
2. Solve the right triangle. O H
SOH – CAH – TOA P PQ QR
x . 22
180 – 90 – 37
c2 = a2 + b2
sin 37° =
222 = a
mP = 53°
22  sin 37° = x
484 = a
13.24 = x
308.7 = a2

7. O A SOH – CAH – TOA P N PN 17 12 c2 = a2 + b2 tan P° =
2. Solve the right triangle. O A
SOH – CAH – TOA P N PN 17 12
c2 = a2 + b2
tan P° =
180 – 90 – 54.8
c2 =
tan P° = 1.42
mN = 35.2°
c2 =
P° = tan-1 (1.42)
c2 = 433
P° = 54.8°

8. A H SOH – CAH – TOA ST U UT x . 15 c2 = a2 + b2 cos 70° =
2. Solve the right triangle. A H
SOH – CAH – TOA ST U UT
x . 15
180 – 90 – 70
c2 = a2 + b2
cos 70° =
152 = a
mU = 20°
15  cos 70° = x
225 = a
5.13 = x
= a2

9. O H SOH – CAH – TOA U E UM c2 = a2 + b2 15 18 sin U° =
2. Solve the right triangle. O H
SOH – CAH – TOA U E UM
c2 = a2 + b2 15 18
sin U° =
180 – 90 – 56.4
182 = a
sin U° = 0.833
mE = 33.6°
324 = a
U° = sin-1 (0.83)
99 = a2
U° = 56.4°

10. A H SOH – CAH – TOA S U UT c2 = a2 + b2 7.5 31.3 cos S° =
2. Solve the right triangle. A H
SOH – CAH – TOA S U UT
c2 = a2 + b2
7.5
31.3
cos S° =
180 – 90 – 76.1
31.32 = a
cos S° = 0.24
mU = 13.9°
979.69= a
S° = cos-1 (0.24)
= a2
S° = 76.1°