# In a right-angled triangle ABC (angle C is 90 degrees), angle A is twice the angle B

July 24, 2021 | education

| **In a right-angled triangle ABC (angle C is 90 degrees), angle A is twice the angle B, the hypotenuse of AB is 18 degrees. Find the AC leg.**

Given:

Right-angled triangle ABC,

angle С = 90 degrees,

angle A = 2 * angle B,

AB = 18.

Find the length of the AC leg -?

Solution:

1) Consider a right-angled triangle ABC.

We know that the sum of the degree measures of any triangle is 180 degrees. Consequently:

angle A + angle B + angle C = 180;

2 * angle B + angle B + 90 = 180;

2 * angle B + angle B = 90;

3 angles B = 90;

angle B = 90: 3;

angle B = 30 degrees;

2) In a right-angled triangle opposite an angle of 30 degrees lies a leg, which is half the hypotenuse. Then AC = 1/2 * AB;

AC = 1/2 * 18;

AC = 9.

Answer: AC = 9.

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