Question

Suppose a triangle has side lengths b = 95.9, and c = 6.1. Suppose the measure of angle B is 124 degrees and the measure of angle A is 53 degrees. Which of the following answers is closest to the length of side a?

Answer 1

To determine the length of side a in the given triangle, the Law of Sines is used, resulting in an approximate value of 93.8 for the length of side a.

Step-by-step explanation:

To find the length of side a in the given triangle, we can use the Law of Sines, which states that the ratio of the length of a side to the sine of its opposite angle is constant for all three sides of a triangle. The formula is given by:

a/sin(A) = b/sin(B) = c/sin(C)

Since the sum of angles in a triangle is 180 degrees, we can find angle C by subtracting the given angles from 180 degrees:

Angle C = 180 degrees - Angle A - Angle B
= 180 degrees - 53 degrees - 124 degrees
= 3 degrees

Now applying the Law of Sines:

a / sin(53 degrees) = 95.9 / sin(124 degrees)

Multiplying both sides by sin(53 degrees) gives:

a = 95.9 * sin(53 degrees) / sin(124 degrees)

Using a calculator, we find that the length of side a is approximately:

a ≈ 95.9 * 0.7986 / 0.8192
≈ 93.8

The closest length of side a is approximately 93.8.