Final answer:
To find the length of side b in triangle δABC, the Law of Sines is used, applying the given angles and the length of side a. Measure of angle A is found by subtracting the sum of angles B and C from 180 degrees. Then, the Law of Sines ratio is solved for the length of b.
Step-by-step explanation:
The student is asking for the length of side b in triangle δABC when given the measure of angle B as 84 degrees, the measure of angle C as 46 degrees, and the length of side a as 16 inches. To find the length of side b, 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 the same for all sides of a triangle.
First, calculate the measure of angle A by using the fact that the sum of angles in a triangle is 180 degrees. Measure of angle A = 180 - ( Measure of angle B + Measure of angle C) = 180 - (84 + 46) = 50 degrees.
Next, using the Law of Sines, the length of side b is determined by the following ratio:
sin(A) / a = sin(B) / b
Applying the values:
sin(50°) / 16 inches = sin(84°) / b
Rearranging to find length of b:
b = (sin(84°) * 16 inches) / sin(50°)
By calculating this, you will get the length of side b, which should be one of the options provided by the student.