In triangle ABC, angle C = 90 degrees, CH – height, AC = 4, AH = √7. Find: cosВ.

Let us determine what the height of CH will be equal to, when from the condition of the task we know that the length of the AS side is 4, while the length of AH is equal to √7:

√ (4 ^ 2 – (√7) ^ 2) = √ (16 – 7) = √9 = 3.

Let us determine what the tangent of angle A will equal:

3: √7 = 3 / √7.

Let us determine what, in this case, the side CB of the triangle ABC will equal:

CB / AC = tg A;

CB = 4 * 3 / √7 = 12 / √7.

Determine what the sine of angle B will equal:

3: 12 / √7 = √7 / 4.

Let us determine what the cosine of the angle B will be:

√ (1 – (√7 / 4) ^ 2) = √9 / 16 = 3/4.

Answer: 3/4.