In an isosceles triangle ABC with base AB = 10, the height BK is lowered from the top B. Find cos A if BK = 4√6.

1. Consider triangle ABC, it is isosceles, it follows from this that <A = <C. Also because of this cos A = cos B.

2. Consider the triangle AKВ, it is a right-angled triangle. It is known that AK is a perpendicular to the BC.

3. Find cos B. Let’s write the formula: cos B = BK / AB. Since we found out above that cos A = cos B, we can find cos A.

4. Find:
cos A = 8/32;
cos A = 1/4;
cos A = 0.25.

Answer: cos A = 0.25.