Question

In triangle ABC, what is the measure of angle C if side a is 22, side b is 19, and angle A is 52°?

Answer 1

The measure of angle C in triangle ABC is 76°.

Step-by-step explanation:

In a triangle, the sum of all interior angles is always 180°. Therefore, we can find angle C by subtracting the measures of angles A and B from 180°.

∠C = 180° - ∠A - ∠B

We are given that angle A is 52°, and to find angle B, we can use the law of sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. In mathematical terms:

`sinAa​ = sinBb​ = sinCc​`

Given sides a and b, and angle A, we can rearrange the formula to find sin B:

`sinB= ab⋅sinA​`

Substituting the given values:

`sinB= ab⋅sinA​`

After calculating sin B, we can find angle B using the inverse sine function:

`∠B=sin −1 (sinB)`

Now that we have angle A and angle B, we can substitute them into the first formula to find angle C:

∠C = 180° - 52 - ∠B

After performing the calculations, we find that angle C is 76°.