In triangle ABC, angle C is 90 degrees, AC = 3, sin A = 3/5 Find BC.

Find BC in triangle ABC if the values are known:

Angle C is 90 °;
AC = 3;
sin A = 3/5.
1) The ratio of the adjacent leg AC to the hypotenuse AB is equal to the cosine of angle A.

We get the formula in the form:

cos A = AC / AB, where cos A = √ (1 – sin ^ 2 A) = √ (1 – (3/5) ^ 2 = √ (1 – 0.6 ^ 2) = √ (1 – 0.36) = √ (0.64) = 0.8;

That is, cos A = 0.8.

2) Find AB from the formula cos A = AC / AB.

AB = AC / cos A = 3 / (0.8) = 3 / (4/5) = 3 * 5/4 = 15/4;

3) Find the BC by the Pythagorean theorem.

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

(15/4) ^ 2 = BC ^ 2 + 3 ^ 2;

BC ^ 2 = 225/16 – 9;

BC ^ 2 = 81/16;

BC = 9/4.