The height AH of a right-angled triangle ABC drawn to the hypotenuse is 7 cm, and the angle c is 60 °. find AB.

1. By the theorem, the sum of the angles of a triangle:
angle A + angle B + angle C = 180 degrees;
90 + angle B + 60 = 180;
angle B = 180 – 150;
angle B = 30 degrees.
2. Consider triangle АНВ: angle АНВ = 90 degrees (since АН is perpendicular to BC), angle АНВ (angle В) = 30 degrees, АН = 7 cm – leg, AB – hypotenuse (since it lies opposite an angle equal to 90 degrees ).
From the properties of a right-angled triangle, it is known that opposite an angle of 30 degrees lies a leg, which is half the hypotenuse.
Then:
AH = AB / 2;
AB / 2 = 7;
AB = 7 * 2;
AB = 14 cm.
Answer: AB = 14 cm.