In a right-angled triangle ABC, the angle C is a straight line, the difference BA-BC is 8 cm.

In a right-angled triangle ABC, the angle C is a straight line, the difference BA-BC is 8 cm. Find the hypotenuse AB if the angle A = 30 degrees.

Let us express AB through the sin function.

The sine of the angle is the ratio of the opposite leg to the hypotenuse:

Sin A = BC: AB;

Find AB if A = 30 °.

AB = BC: sin 30 °;

Sin 30 ° = ½;

AB = BC: ½;

AB = 2 × BC;

By condition, the difference between AB and BC is 8 cm:

AB – BC = 8 cm;

AB = BC + 8;

In the equations AB = 2 × BC and AB = BC + 8, the right-hand sides are equal.

Let’s equalize the left sides and solve the resulting equation:

2 × BC = BC + 8;

2 × BC – BC = 8;

BC = 8 cm;

AB = 2 × 8 = 16 cm.

Let’s check:

AB – BC = 16 – 8 = 8 cm – the problem was solved correctly.