In an isosceles triangle ABC with a base AC, the lateral side AB is 10, and the cos of angle A is 4/5.

In an isosceles triangle ABC with a base AC, the lateral side AB is 10, and the cos of angle A is 4/5. Find the height drawn to the base.

1. Draw the height BH from the top B to the bottom AC;

2. Consider a triangle ABH:

AB = 10;

AH, BH – legs; AB – hypotenuse;

The cosine of the angle is the ratio of the adjacent leg to the hypotenuse;

cos∠A = AH: AB;

3. Find the height BH:

4/5 = AH: 10;

AH = 4/5 * 10 = 8.

Answer: 8.




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