In an isosceles triangle ABC with base AC, the side AB is 17 and cos A = 8/17.

In an isosceles triangle ABC with base AC, the side AB is 17 and cos A = 8/17. Find the height drawn to the base.

In an isosceles triangle ABC, it is known:

Founding AC;
Side AB = 17;
cos A = 8/17.
Let’s find the height of the HВ, drawn to the base of the speaker.

Decision:

Consider a triangle ABН with a right angle Н.

Angle H = 90 °;

Since cos A is known, then we find sin A

sin A = √ (1 – cos ^ 2 A) = √ (1 – (8/17) ^ 2) = √ (1 – 64/289) = √ (289/289 – 64/289) = √ (289 – 64) / √289 = √225 / √289 = 15/17;

sin A = BH / AB;

Let us express ВН from here.

BH = AB * sin A;

Plug in the known values and calculate the height value.

BH = 17 * 15/17 = 17/17 * 15 = 1 * 15 = 15;

Answer: BH = 15.