# In a right-angled triangle, the leg is 18 cm, the opposite angle is 30 degrees. find angle A and sides AC and AB

September 30, 2021 | education

| From the condition it is known that in a right-angled triangle the leg is 18 cm, the opposite angle is 30 °. And we need to find the angle A and sides AC and AB.

We start by calculating the angle A. By the theorem on the sum of the angles of a triangle, we subtract from 180 ° the sum of the right angle and an angle of 30 °.

angle A = 180 ° – 90 ° – 30 ° = 60 °.

To find the sides, we apply the theorem that a leg lying opposite an angle of 30 ° is equal to half the hypotenuse.

We can find the hypotenuse by multiplying the known leg by 2.

AB = 18 * 2 = 36 cm hypotenuse.

We are looking for the second leg by the Pythagorean theorem:

AC = √ (AB ^ 2 – BC ^ 2) = √ (36 ^ 2 – 18 ^ 2) = √ (1296 – 324) = √972 = 6√27 cm.

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