Mathematics: Using the provided measures determine the measure of angle K. A)30.5° B)34.90 C)41.2° D)58.0°

Using the provided measures determine the measure

Beast3dgar

18.04.2021

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:

$\frac{sin(K)}{GF} = \frac{sin(G)}{KF}$

Substitute

$\frac{sin(K)}{3.18} = \frac{sin(64)}{5}$

Multiply both sides by 3.18

$sin(K) = \frac{sin(64)}{5}*3.18$

sin(K) = 0.5716

$K = sin^{-1}(0.5716)$

K = 34.8618741° ≈ 34.90°

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