In the triangle ABC AC = BC, AB = 30, cosA = 0.6 find the height AH

By condition, the two sides of the triangle are equal, which means the triangle is isosceles, the angles at the base are equal:

BAC = ABC.

The values of the cosines of these angles are also equal.

Cos A = cos B = 0.6.

Cosine is the ratio of the adjacent leg to the hypotenuse

In a right-angled triangle ABH – adjacent leg BH, hypotenuse AB = 30 cm:

Cos B = BH: AB;

BH = AB × cos B;

BH = 30 x 0.6;

BH = 18 cm.

Find AH by the Pythagorean theorem:

AB ^ 2 = BH ^ 2 + AH ^ 2;

AH ^ 2 = AB – BH;

AH ^ 2 = 30 ^ 2 – 18 ^ 2;

AH ^ 2 = 900-324;

AH ^ 2 = 576;

AH = √576;

AH = 24 cm.