In an isosceles triangle ABC base AC 24 tangent 0.75, find the area of triangle ABC.

1) Draw the height from point B to the base of the speaker. The HВ height in an isosceles triangle divides the AC side in half.

2) Find the side of AН.

AH = 1/2 * AC = 1/2 * 24 = 24/2 = 12.

3) Calculate the height of the BH of an isosceles triangle.

tg a = AH / BH;

BH * tg a = AH;

Hence, BH = AH / tg a = 12 / 0.75 = 12 / (3/4) = 12 * 4/3 = 12/3 * 4 = 4 * 4 = 16;

4) The area of an isosceles triangle ABC is found by the formula:

S = 1/2 * AC * ВН = 1/2 * 24 * 16 = 24/2 * 16 = 12 * 16 = 10 * 16 + 2 * 16 = 160 + 32 = 192.

Answer: S = 192.