# In triangle ABC, angle C is 90 degrees AB = 5, sin A = 3/5 find AC

September 29, 2021 | education

| Given:

right-angled triangle ABC;

angle C = 90;

sin A = 3/5;

AB = 5;

Find: AC -?

Solution:

1) Consider a right-angled triangle ABC. The sine of the angle in a right-angled triangle is equal to the ratio of the opposite leg to the hypotenuse. Hence:

sin A = BC / AB;

BC = sin A * AB;

BC = 3/5 * 5;

BC = (3 * 5) / 5;

BC = (3 * 1) / 1;

BC = 3;

2) by the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):

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

AC ^ 2 = AB ^ 2 – BC ^ 2;

AC ^ 2 = 5 ^ 2 – 3 ^ 2;

AC ^ 2 = 25 – 9;

AC ^ 2 = 16;

AC = 4.

Answer: AC = 4.

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