In a right-angled triangle ABC, angle C = 90, angle A = 30 CD-height, AB = 16. Find BD.

Since the triangle ABC is rectangular, and the angle CAB = 30 °, the leg CB, which lies opposite the angle CAB, is equal to half of the hypotenuse AB.

So we get that СВ = 1/2 * AB = 1/2 * 16 = 8 cm.

The sum of all the angles of the triangle is 180 °, which means that the angle ABC = 180 ° – 90 ° – 30 ° = 60 °.

Consider triangle CDB: the triangle is right-angled because CD is the height to AB.

Find the DCB angle:

angle DCB = 180 ° – 90 ° – 60 ° = 30 °.

Opposite an angle of 30 ° lies the leg BD, equal to half of the hypotenuse CB.

So we get one hundred BD = 1/2 * CB = 1/2 * 8 cm = 4 cm.

Answer: BD = 4 cm.