In triangle ABC AC = BC = 3√5, height CH = 3. Find tgA.

Consider the ACN triangle: the angle H is 90 ° (CH – height), which means the ACN triangle is rectangular.

According to the Pythagorean theorem: AH² = AC² – CH²;

AC = 3√5; CH = 3. AH² = (3√5) ² – 3² = 9 * 5 – 9 = 45 – 9 = 36.

AH = 6.

The tangent is equal to the ratio of the opposite leg to the adjacent one:

tgА = СН / АН = 3/6 = 1/2.

Answer: the tangent of angle A is 1/2.