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?

Question

Sarah

Mathematics

27 May, 05:38

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?

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Answers (1)

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Barkley · Answer 1

AC = 18

Step-by-step 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