Triangle a b c is shown. the length of a b is 12, the length of b c is 24, and the length of c a is 12 startroot 3 endroot what are the angle measures of triangle abc? m∠a = 30°, m∠b = 60°, m∠c = 90° m∠a = 90°, m∠b = 60°, m∠c = 30° m∠a = 60°, m∠b = 90°, m∠c = 30° m∠a = 90°, m∠b = 30°, m∠c = 60°

m∠A = 90°, m∠B = 60°, m∠C = 30°

Step-by-step explanation:

step 1

see the attached figure to better understand the problem

In this problem we have a right triangle, because the Pythagorean Theorem is satisfied

so

therefore

step 2

Find the measure of angle B

we know that

In the right triangle ABC

----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

step 3

Find the measure of angle C

we know that

----> by complementary angles

we have

substitute

therefore

m∠A = 90°, m∠B = 60°, m∠C = 30°

step-by-step explanation: