Question

Using the provided measures determine the measure of angle K.

A)30.5°
B)34.90
C)41.2°
D)58.0°

Answer 1

B. 34.90°

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:

`(sin(K))/(GF) = (sin(G))/(KF)`

Substitute

`(sin(K))/(3.18) = (sin(64))/(5)`

Multiply both sides by 3.18

`sin(K) = (sin(64))/(5)*3.18`

`sin(K) = 0.5716`

`K = sin^(-1)(0.5716)`

K = 34.8618741° ≈ 34.90°