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

A triangle in which one angle is 90º is called rectangular.

To calculate the AC leg, we use the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AB ^ 2 = BC ^ 2 + AC ^ 2;

AC ^ 2 = AB ^ 2 – BC ^ 2.

To do this, you need to find the length of the BC leg. Let’s apply the sine theorem. The sine of an acute angle of a right triangle is the ratio of the opposite leg to the hypotenuse:

sin A = BC / AB;

BC = AB ∙ sin A;

BC = 5 * 3/5 = 15/5 = 3 cm.

AC2 = 52 – 32 = 25 – 9 = 16;

AC = √16 = 4 cm.

Answer: The length of the speaker is 4 cm.