In triangle ABC, angle C is 90 degrees, sinA = 3/5, AC = 4. Find AB.

Given:

ABC – right triangle;

Angle C = 90 degrees;

AC = 4;

sin A = 3/5;

Find AB.

Decision:

1) Find cos a from the formula cos ^ 2 a + sin ^ 2 a = 1;

Hence, cos a = √ (1 – sin ^ 2 a) = √ (1 – (3/5) ^ 2) = √ (1 – 0.6 ^ 2) = √ (1 – 36) = √0.64 = 0.8;

2) 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 = 4 / 0.8 = 4 / (8/10) = 4/1 * 10/8 = 4/8 * 10 = 1/2 * 10 = 5;

Answer: AB = 5.