In an isosceles triangle ABC, the base AC is 16. AB = 10. Find the Sin of angle A.

Draw the height BK from the vertex of an isosceles triangle ABC.

BK is also the median (by the property of an isosceles triangle).

AK = 16: 2 = 8.

The sine of the angle is the ratio of the opposite leg to the hypotenuse.

In triangle ABK, the angle is K = 90 °, so sin A = BK: AB.

Find BK by the Pythagorean theorem.

BK = √ (AB ^ 2 – AK ^ 2),

BK = √ (10 ^ 2 – 8 ^ 2) = √ (100 – 64) = √36 = 6.

Then sin A = 6: 10 = 0.6.