In triangle ABC it is known that angle C = 90 degrees, angle A = 30 degrees, CD – height, BD = 7cm. Find the hypotenuse AB.

Consider the resulting right-angled triangle CBD:

since the angle B = 60 °, the hypotenuse of BC is twice the adjacent leg BD, because the cosine of 60 ° is 0.5:

BC = BD * 2 = 7 * 2 = 14 cm;

now we find the hypotenuse AB of a right-angled triangle ABC, which is twice the leg BC, because the cosine of 60 ° is 0.5:

AB = BC * 2 = 14 * 2 = 28 cm.