In triangles ABC AC = BC, AB = 15, AH-height, BH = 3. Find cosBAC.

In triangles ABC it is known:

AC = BC;
AB = 15;
AH – height;
BH = 3.
Find cos BAC.

Decision:

1) Since the triangle is isosceles, then in the triangle ABC angle A and angle B are equal.

Angle A = Angle B = Angle BAC;

2) Consider triangle АНВ with right angle H.

In this triangle, AB = 15 and BH = 3 are known.

AH = √ (AB ^ 2 – BH ^ 2) = √ (15 ^ 2 – 3 ^ 2) = √ ((15 – 3) * (15 + 3)) = √ (12 * 18) = √216 = √ (36 * 6) = 6 * √6 = 6√6;

3) cos B = BH / AB = 3/15 = 3 / (5 * 3) = 1 / (5 * 1) = 1/5 = 0.2;

Since cos B = 0.2, then cos CAB = 0.2.