In triangle ABC, angle C is 90, tga = 3 √7 / 7. Find cosB.

By condition, a right-angled triangle ABC with an angle C = 90 ° is given. It is known that:

tg (∠A) = 3 * √7 / 7;

It is required to calculate the value of cos (∠B).

Note that in a right-angled triangle:

∠A + ∠B = 90 °;

or

∠В = 90 ° – ∠A;

Using trigonometric equalities:

cos (∠В) = cos (90 ° – ∠A) = sin (∠A);

sin (∠A) = tg (∠A) / √ (1 + tg2 (∠A));

Substituting the original value, we get:

sin (∠A) = (3 * √7 / 7) / √ (1 + (3 * √7 / 7) 2) = (3 / √7) / √ (16/7) = 3/4;

Accordingly, we obtain

cos (∠В) = sin (∠A) = ¾;

Answer: cos (∠В) = 3/4