In a right-angled triangle ABC, the angle C is a straight line, the difference BA-BC is 8 cm.
August 31, 2021 | education|
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.
AB – BC = 16 – 8 = 8 cm – the problem was solved correctly.
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