Given , , and , use the Law of Sines to solve the triangle (if possible) for the value of b. If two solutions exist, find both. Round answer to two decimal places.
E)not possible

Question

Given  ,  , and  , use the Law of Sines to solve the triangle (if possible) for the value of b. If two solutions exist, find both. Round answer to two decimal places.
E)not possible

Quizplus · Accepted Answer

Using the Law of Sines:
$$\frac{b}{\sin A}=\frac{c}{\sin B}$$
For the given values, we have: 
$$\frac{b}{\sin(11ec1854_fd53_f572_acfc_f54f788f2d98_TBX8702_11)}=\frac{c}{\sin(11ec1854_fd53_f573_acfc_293a9f6a9562_TBX8702_11)}$$
and
$$\frac{b}{\sin(11ec1854_fd53_f572_acfc_f54f788f2d98_TBX8702_11)}=\frac{a}{\sin(11ec1854_fd53_f574_acfc_c578d217a786_TBX8702_11)}$$
Since we are solving for b, we can set the two equations equal to each other:
$$\frac{c}{\sin(11ec1854_fd53_f573_acfc_293a9f6a9562_TBX8702_11)}=\frac{a}{\sin(11ec1854_fd53_f574_acfc_c578d217a786_TBX8702_11)}$$
Solving for c:
$$ c=\frac{a\sin(11ec1854_fd53_f573_acfc_293a9f6a9562_TBX8702_11)}{\sin(11ec1854_fd53_f574_acfc_c578d217a786_TBX8702_11)}$$
Plugging in the given values:
$$c=\frac{\sqrt{2}\sin(150)}{\sin(135)}\approx 1.33$$
Now we can use the Law of Sines to solve for b:
$$ b=\frac{c\sin A}{\sin B}$$
Plugging in the values we have found:
$$ b=\frac{1.33\sin(150)}{\sin(105)} \approx 2.29$$
Therefore, the answer is C, and b is approximately 2.29.

Given , , and , Use the Law