Question

In the right triangle shown, m ∠ A = 30 ° m∠A=30°m, angle, A, equals, 30, degree and A B = 12 3 AB=12 3 ​ A, B, equals, 12, square root of, 3, end square root. 30 ° 30° x x 12 3 12 3 ​ C C A A B B How long is A C ACA, C?

Answer 1

the proof is in the picture

Explanation:

Answer 2

AC = 18

Explanation:

Given the question:

In a right triangle, m∠A = 30° and AB = 12√3 (AB is the hypotenuse). How long is AC?

Side AC is adjacent to angle A. Then, by definition of cosine:

cos(A) = adjacent/hypotenuse

cos(A) = AC/AB

AC = cos(A)*AB

AC = cos(30°)*12√3

AC = 18