# In an isosceles triangle ABC with a base BC, the length of the lateral side and the length of the height

**In an isosceles triangle ABC with a base BC, the length of the lateral side and the length of the height drawn to the lateral side are given. AB = 29, CH = 20. Find the length of the side BC if it is known that the angle at the vertex A is obtuse.**

Since angle A is obtuse, the height CH is drawn to the continuation of side AB.

The ABC triangle is isosceles, then AC = AB = 29 cm.

In a right-angled triangle ACH, according to the Pythagorean theorem, we determine the length of the segment AH.

AH ^ 2 = AC ^ 2 – CH ^ 2 = 29 ^ 2 – 20 ^ 2 = 841 – 400 = 441.

AH = 21 cm.

Then the length of the segment BH = AB + AH = 29 + 21 = 50 cm.

From the right-angled triangle ВСН, according to the Pythagorean theorem, we determine the length of the base ВС.

BC ^ 2 = BH ^ 2 + CH ^ 2 = 50 ^ 2 + 20 ^ 2 = 2500 + 400 = 2900.

BC = 10 * √34 cm.

Answer: The length of the base of the BC is 10 * √29 cm.