Question

In triangle abc, a is a right angle, and ab = 16√3, and the measure of b=30 degrees. What is the length of ac.

Answer 1

the length of ac is 16.

Explanation:

Given;

A is right angle, = 90⁰

B is 30⁰

ab = 16√3

C

↓

↑

A → ← B

If this right angle triangle is considered, length bc is the hypotenuse and length ac is the opposite side of angle B.

The length of ac is calculated as follows;

`tan \ B = (opposite \ side)/(adjacent \ side) \\\\tan \ B = (ac)/(ab) \\\\ac = ab \ * \ tan \ B\\\\ac = 16√(3) \ * (√(3) )/(3) \\\\ac = (16 √(9) )/(3) \\\\ac = (16 * 3)/(3) \\\\ac = 16`

Therefore, the length of ac is 16.