Given $A = 52 ^ { \circ } , B = 65 ^ { \circ }$, and $a = 7.1$, use the Law of Sines to solve the triangle for the value of $b$. Round answer to two decimal places.

A) $b = 6.98$
B) $b = 8.03$
C) $b = 6.28$
D) $b = 8.17$
E) $b = 6.17$

Question

Given $A = 52 ^ { \circ } , B = 65 ^ { \circ }$, and $a = 7.1$, use the Law of Sines to solve the triangle for the value of $b$. Round answer to two decimal places.

A) $b = 6.98$ 
B) $b = 8.03$ 
C) $b = 6.28$ 
D) $b = 8.17$ 
E) $b = 6.17$

Quizplus · Accepted Answer

By the Law of Sines, we have:

$$\dfrac{a}{\sin A} = \dfrac{b}{\sin B}$$

Plug in the given values:

$$\dfrac{7.1}{\sin 52^\circ} = \dfrac{b}{\sin 65^\circ}$$

Solve for $b$:

$$b = \dfrac{7.1\sin 65^\circ}{\sin 52^\circ} \approx 8.17$$

Therefore, the answer is D, $b=8.17$.

Given A=52∘,B=65∘A = 52 ^ { \circ } , B = 65 ^ { \circ }A=52∘,B=65∘

Given $A = 52 ^ { \circ } , B = 65 ^ { \circ }$