If $B = 20 ^ { \circ } \text { and } a = 8$ , determine the value of b. Round to two decimal places.
A) 7.52
B) 2.74
C) 2.91
D) 8.51
E) 21.98

Question

If $B = 20 ^ { \circ } \text { and } a = 8$ , determine the value of b. Round to two decimal places. 
A) 7.52 
B) 2.74 
C) 2.91 
D) 8.51 
E) 21.98

Quizplus · Accepted Answer

Using the sine ratio, we have:
$$\frac{b}{\sin B} = \frac{a}{\sin A}$$
Since $B = 20 ^{ \circ }$ and $A = 180 ^{ \circ } - 90 ^{ \circ } - B = 70 ^{ \circ }$, we have:
$$\frac{b}{\sin 20 ^{ \circ }} = \frac{8}{\sin 70 ^{ \circ }}$$
Solving for $b$, we get:
$$b = 8 \cdot \frac{\sin 20^{ \circ }}{\sin 70^{ \circ }} \approx 2.91$$
Rounding to two decimal places, we have $b \approx 2.91$, which corresponds to choice C.

If B=20∘ and a=8B = 20 ^ { \circ } \text { and } a = 8B=20∘ and a=8

If $B = 20 ^ { \circ } \text { and } a = 8$