Question

Solve for x... need as fast as you can do it.

Answer 1

6. 21.0°

7. 39.6°

8. 58.0°

9. 72.9°

Explanation:

6. Reference angle (θ) = x°

Hypotenuse = 15

Adjacent = 14

Apply CAH:

`Cos(\theta) = (Adjacent)/(Hypotenuse)`

Plug in the values

`Cos(x) = (14)/(15)`

`x = Cos^(-1)((14)/(15))`

x ≈ 21.0° (nearest tenth)

7. Reference angle (θ) = x°

Opposite = 19

Adjacent = 23

Apply TOA:

`Tan(\theta) = (Opposite)/(Adjacent)`

Plug in the values

`Tan(x) = (19)/(23)`

`x = Tan^(-1)((19)/(23))`

x ≈ 39.6° (nearest tenth)

8. Reference angle (θ) = x°

Hypotenuse = 17

Adjacent = 9

Apply CAH:

`Cos(\theta) = (Adjacent)/(Hypotenuse)`

Plug in the values

`Cos(x) = (9)/(17)`

`x = Cos^(-1)((9)/(17))`

x ≈ 58.0° (nearest tenth)

9. Reference angle (θ) = x°

Opposite = 43

Hypotenuse = 45

Apply SOH:

`Sin(\theta) = (Opposite)/(Hypotenuse)`

Plug in the values

`Sin(x) = (43)/(45)`

`x = Sin^(-1)((43)/(45))`

x ≈ 72.9° (nearest tenth)