Please Help! Unit 8: Right Triangles & Trigonometry Homework 7

How can we find the measure of angle C?

We have the following information: a = 12, b = 10, c = 15, A = 30 degrees, B = 60 degrees.

What is the measure of angle C?

Measure of angle C:

To find the measure of angle C, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In this case, we are given side lengths and angle measures, so we can use the Law of Sines formula.

Let's use the Law of Sines formula: a/sin(A) = b/sin(B) = c/sin(C).

Substitute the given values into the formula: 12/sin(30) = 10/sin(60) = 15/sin(C).

Calculate sin(30) and sin(60) to get: 12/(1/2) = 10/(√3/2) = 15/sin(C).

This simplifies to: 24 = 20√3 = 15/sin(C).

Solve for sin(C) by dividing 15 by 20√3: sin(C) ≈ 15/(20√3).

Use a calculator to find sin(C) ≈ 0.433. Since sin(C) = opposite/hypotenuse, we get sin(C) = c/b. Substitute the values of c and b to get: 0.433 = 15/b. Solve for b to find b ≈ 15/0.433 ≈ 34.64.

Therefore, the measure of angle C is approximately 34.64 degrees.