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:
[tex] Cos(\theta) = \frac{Adjacent}{Hypotenuse} [/tex]
Plug in the values
[tex] Cos(x) = \frac{14}{15} [/tex]
[tex] x = Cos^{-1}(\frac{14}{15}) [/tex]
x ≈ 21.0° (nearest tenth)
7. Reference angle (θ) = x°
Opposite = 19
Adjacent = 23
Apply TOA:
[tex] Tan(\theta) = \frac{Opposite}{Adjacent} [/tex]
Plug in the values
[tex] Tan(x) = \frac{19}{23} [/tex]
[tex] x = Tan^{-1}(\frac{19}{23}) [/tex]
x ≈ 39.6° (nearest tenth)
8. Reference angle (θ) = x°
Hypotenuse = 17
Adjacent = 9
Apply CAH:
[tex] Cos(\theta) = \frac{Adjacent}{Hypotenuse} [/tex]
Plug in the values
[tex] Cos(x) = \frac{9}{17} [/tex]
[tex] x = Cos^{-1}(\frac{9}{17}) [/tex]
x ≈ 58.0° (nearest tenth)
9. Reference angle (θ) = x°
Opposite = 43
Hypotenuse = 45
Apply SOH:
[tex] Sin(\theta) = \frac{Opposite}{Hypotenuse} [/tex]
Plug in the values
[tex] Sin(x) = \frac{43}{45} [/tex]
[tex] x = Sin^{-1}(\frac{43}{45}) [/tex]
x ≈ 72.9° (nearest tenth)
