In a right-angled triangle ABC with a right angle C, the sine of an acute angle A is 4/5. Find the tangent of angle B.

univerkov | February 4, 2021 | education

Let us denote the hypotenuse of a right-angled triangle by c, then BC and AC are projections:

BC = c * sin (A) = c * 4/5;

AC = c * cos (A) = c * (1 – cos ^ 2 (A)) = c * 3/5.

Then:

tg (B) = AC / CB = 3/5 * c: 4/5 * c = 3/4.

Answer: the required tangent of angle B is 3/4.

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