In a triangle ABC, the angle is A = B = 75 °. Find the length BC if the area of the triangle is 36 cm².

1. From the top B we draw the height BH to the AC side.

2. Triangle ABC is isosceles, since angles A and B at the base of AB are equal.

Therefore AC = BC.

2. Angle C = 180 ° – 75 ° – 75 ° = 30 °.

2. In the BCH triangle, the BH leg is opposite an angle of 30 °. Consequently, its length is half the length of the BC hypotenuse:

ВН = ВС / 2.

3. The area of the triangle ABC = AC x BH / 2 = 36 cm ^ 2. Replace AC for BC, ВН for BC / 2:

BC x BC / 2: 2 = 36.

BC ^ 2 = 144.

BC = √144 = 12 cm.

Answer: the length of the BC side is 12 cm.