In a right-angled triangle, angle A = 30 °, side BC = 4 cm. Find side AB.

In a right-angled triangle with an angle of 30 degrees, the leg opposite this angle is half the hypotenuse.

angle A = 30 0, the opposite leg BC = 4 cm. hence the hypotenuse AB = 2 * BC = 8 cm.

2 solution

According to the definition of trigonometric functions, the sine is the ratio of the opposite leg to the hypotenuse:

Sin A = BC / AC; (one)

from here:

AC = BC / sin A;

we know that:

Sin A = sin 30 O = 1/2 = 0.5;

we substitute the numerical values into formula (1) and find the required hypotenuse:

AC = BC / 0.5 = BC * 2 = 4 * 2 = 8 (cm).