In a triangle ABC, the angle is C = 90 degrees, AB = 8 / √7, sinB = 3/4. Find the height CH.

In triangle ABC, we find the height of CH, if it is known:

Angle C = 90 °;
AB = 8 / √7;
sin B = 3/4.
Decision:

1) sin B = AC / AB (the ratio of the opposite leg to the hypotenuse);

AC = AB * sin B = 8 / √7 * 3/4 = 8/4 * 3 / √7 = 2 * 3 / √7 = 6 / √7;

2) Find the BC leg according to the Pythagorean theorem.

ВС = √ (AB ^ 2 – AC ^ 2) = √ ((8 / √7) ^ 2 – (6 / √7) ^ 2) = √ (64/7 – 36/7) = √ (64 – 36 ) / √7 = √ (28/7) = √4 = 2;

3) sin b = CH / BC;

Let us express the height of CH from here.

CH = BC * sin B;

Plug in the known values and calculate the height value.

CH = 2 * 3/4 = 2/4 * 3 = 1/2 * 3 = 3/2 = 1.5;

Answer: CH = 1.5.