# Find the unknown sides and angles of a right-angled triangle if the hypotenuse

Find the unknown sides and angles of a right-angled triangle if the hypotenuse and one of the angles are known: a = 30 cm, angle A = 36 degrees?

Let us denote the right-angled triangle given by the condition ABC, angle C – straight line, AB – hypotenuse.
Let us write in this triangle the definition of the sine of angle A (we take the sine value from the Bradis table):
Sin A = BC / AB → ВС = AB * sin 36 ° = 30 * 0.587785 = 17.63355 ≈ 17.6 (cm).
We will do the same with the cosine of angle A:
Cos A = AC / AB → AC = AB * cos 36 ° = 30 * 0.809017 = 24.27051 ≈ 24.3 (cm).
The second acute angle B is equal to: 90 ° – ∠A = 54 °.
Answer: the legs of the triangle are 17.6 cm, 24.3 cm, angle B 54 °.

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