In a right-angled triangle ABC with a right angle C, the sine of an acute angle A is 3/5. Find the tangent of angle B.

univerkov | September 2, 2021 | education

We denote by b the leg of the triangle, then its hypotenuse is equal to:

b / sin (A) = b: 3/5 = 5 / 3b.

Since the triangle is rectangular, we find the second leg according to the Pythagorean theorem:

√ (5 / 3b) ^ 2 – (b) ^ 2 = 4 / 5b.

Then, by the definition of the tangent, we get:

tg (B) = b: 4 / 5b = 5/4.

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