Question

The area of triangle ABC is 15. If a=12 and b=5, find the measure of angle C.

Answer 1

The measure of angle C in triangle ABC is 30 degrees, calculated by Using the area of the triangle and the sine rule.

Step-by-step explanation:

To find the measure of angle C in triangle ABC, where the area of the triangle is 15 and sides a and b are 12 and 5 respectively, we can use the formula for the area of a triangle: Area = 1/2 * a * b * sin(C). By substituting the given values into the formula, we have:

15 = 1/2 * 12 * 5 * sin(C)

Solving for sin(C), we get:

sin(C) = 15 / (1/2 * 12 * 5)

sin(C) = 15 / 30

sin(C) = 0.5

Now, we need to find the angle whose sine is 0.5. Using a calculator or trigonometry tables, we can determine that:

Angle C = sin-1(0.5) = 30°

Thus, the measure of angle C in triangle ABC is 30 degrees.