In triangle ABC, angle C = 90 degrees, angle A = 30 degrees, AC = 2 ^ 3 find AB.

Given:

ABC – right triangle;

Angle C = 90 °;

Angle A = 30 °;

AC = 2 ^ 3 = 8;

Find AB.

Solution:

In order to find the hypotenuse AB of the triangle ABC, we use the formula:

cos A = AC / AB.

Hence, AB = AC / cos a;

Substitute the known values into the formula and find the hypotenuse AB.

AB = 8 / cos 30 ° = 8 / (√3 / 2) = 8 * 2 / √3 = 16 / √3 = 16 * √3 / (√3 * √3) = 16 * √3 / 3 = 16 / 3 * √3;

Answer: AB = 16/3 * √3.