In an isosceles triangle ABC, the base of the AC is 12, BM is the height of the triangle

In an isosceles triangle ABC, the base of the AC is 12, BM is the height of the triangle, the sine of the MBC angle is 3/4. Find the side of the triangle.

1. Proceeding from the fact that in an isosceles triangle the BM height is the median dividing the base of the AC into two equal parts, we calculate:

AM = CM = 12: 2 = 6 centimeters.

2. Based on the fact that in a right-angled MBC triangle the sine of the MBC angle is the ratio of the MC leg, which is opposite this angle to the BC hypotenuse, we calculate the BC hypotenuse length:

Sine of angle MBC = MC / BC.

6 / BC = 3/4.

BC = 6 x 4/3 = 8 centimeters.

Answer: the lateral side of the BC of the ABC triangle is 8 centimeters.