Side AB is the base of isosceles triangle ABC. Find angle A.

The condition of the problem should look as follows: In an isosceles triangle ABC, the lateral side AB = 17, and the base AC = 16. To find, we need tg of angle A.

Let’s start with a short statement of the problem statement:

triangle ABC – isosceles.

AB = BC = 17;

AC = 16 base.

To find:

tg angle A -?

Let’s start the solution by dropping the perpendicular BH to the base of the isosceles triangle.

Divide point H the base of the triangle into equal parts:

AH = HC = 8.

We apply the Pythagorean theorem to one of the resulting right-angled triangles:

BH ^ 2 = AB ^ 2 – AH ^ 2 = 17 ^ 2 – 8 ^ 2 = 225;

BH = 15.

Let’s find the ratio of the opposite leg to the adjacent one – the tangent of the angle:

tg angle A = BH / AH = 15/8 = 1.875.