Question

Solve each triangle ABC that exists. A = 37° a = 3.7 c = 15.9 Select the correct choice below and, if necessary, fill in the answer boxes within the choice. O A. There are two possible solutions for the triangle. The measurements for the solution with the longer side b are as follows. B, by = The measurements for the solution with the shorter side b are as follows. B =) by = (Round to the nearest tenth as needed.) O B. There is only one possible solution for the triangle. The measurements for the remaining angles B and C and side b are as follows. B= Cu º b= (Round to the nearest tenth as needed.) O C. There are no possible solutions for the triangle.

Answer 1

To solve triangle ABC, use the Law of Sines to find the missing angles and side.

Step-by-step explanation:

To solve the triangle ABC, we can use the Law of Sines. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Using this law, we can find the missing angles and side of the triangle.

1. First, find angle B using the formula sin(B) = (a * sin(C)) / c. Plug in the values a = 3.7, C = 37°, and c = 15.9 to find the value of sin(B).
2. Calculate angle C using the formula C = 180° - A - B. Substitute A = 37° and B from the previous step to find the value of C.
3. Finally, find side b using the formula b = (a * sin(B)) / sin(A). Substitute the known values of a, B, and A to calculate the length of side b.

Based on the given information, there is only one possible solution for the triangle. The measurements for the remaining angles B and C are determined using the Law of Sines, and the length of side b can also be calculated using the same law.

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