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Given δabc with measure of angle b equals 84 degrees comma measure of angle c equals 46 degrees comma and a = 16 inches, what is the length of b? 44.711 inches 20.772 inches 15.025 inches 13.009 inches

User Cantonic
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1 Answer

5 votes

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.

User Lukr
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