B. 34.90°
Step-by-step explanation:
✔️First, find GF using Trigonometric function:
Reference angle = 58°
Adjacent length = GF
Hypotenuse = 6 cm
Apply CAH, thus:
Cos 58 = Adj/Hyp
Cos 58 = GF/6
GF = 6*Cos 58
GF = 3.17951558 ≈ 3.18 cm
✔️Find angle K using the Sine Rule:
![\frac{sin(K)}{GF} = \frac{sin(G)}{KF}](/tpl/images/1206/5955/89b16.png)
Substitute
![\frac{sin(K)}{3.18} = \frac{sin(64)}{5}](/tpl/images/1206/5955/385cf.png)
Multiply both sides by 3.18
![sin(K) = \frac{sin(64)}{5}*3.18](/tpl/images/1206/5955/32feb.png)
![sin(K) = 0.5716](/tpl/images/1206/5955/55ef0.png)
![K = sin^{-1}(0.5716)](/tpl/images/1206/5955/0c1f6.png)
K = 34.8618741° ≈ 34.90°