Question

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

Answer 1

Answer:

6. 21.0°

7. 39.6°

8. 58.0°

9. 72.9°

Step-by-step explanation:

6. Reference angle (θ) = x°

Hypotenuse = 15

Adjacent = 14

Apply CAH:

$Cos(\theta) = \frac{Adjacent}{Hypotenuse}$

Plug in the values

$Cos(x) = \frac{14}{15}$

$x = Cos^{-1}(\frac{14}{15})$

x ≈ 21.0° (nearest tenth)

7. Reference angle (θ) = x°

Opposite = 19

Adjacent = 23

Apply TOA:

$Tan(\theta) = \frac{Opposite}{Adjacent}$

Plug in the values

$Tan(x) = \frac{19}{23}$

$x = Tan^{-1}(\frac{19}{23})$

x ≈ 39.6° (nearest tenth)

8. Reference angle (θ) = x°

Hypotenuse = 17

Adjacent = 9

Apply CAH:

$Cos(\theta) = \frac{Adjacent}{Hypotenuse}$

Plug in the values

$Cos(x) = \frac{9}{17}$

$x = Cos^{-1}(\frac{9}{17})$

x ≈ 58.0° (nearest tenth)

9. Reference angle (θ) = x°

Opposite = 43

Hypotenuse = 45

Apply SOH:

$Sin(\theta) = \frac{Opposite}{Hypotenuse}$

Plug in the values

$Sin(x) = \frac{43}{45}$

$x = Sin^{-1}(\frac{43}{45})$

x ≈ 72.9° (nearest tenth)