In triangle ABC, angle C is 90, sin A = 1/7, AC = 4√3, find AB

Given:

ABC – right triangle;

Angle C = 90 °;

AC = 4√3;

sin A = 1/7;

Find AB.

Decision:

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

cos A = AC / AB.

Hence, AB = AC / cos a = AC / √ (1 – sin ^ 2 a);

Substitute the known values into the formula AB = AC / √ (1 – sin ^ 2 a) and find the hypotenuse AB.

AB = 4√3 / (√ (1 – (1/7) ^ 2) = 4√3 / √ (1 – 1/49) = 4√3 / (49/49 – 1/49) = 4√3 / (√48 / 7) = 4 * √3 * 7 / √48 = 28 * √3 / √48 = 28 * √3 / (√3 * √16) = 28 * 1 / (1 * 4) = 28 / 4 = 7;

Hence, AB = 7.

Answer: AB = 7.