In triangle ABC, angle C is 90 degrees, AC = 10, sin A = 0.8. Find the height CH.

If in triangle ABC from angle C to draw the height CH, then the resulting triangle AНС will be rectangular (angle H is 90 degrees).

It is necessary to consider the AНС triangle. The AC = 10 side lies opposite the right angle and is the hypotenuse. By condition sin A = 0.8.

It is known that sine is a trigonometric function of the angle in a right triangle, equal to the ratio of the leg of the opposite angle to the hypotenuse.

Or sin A = CH / AC,

whence CH = sin A * AC.

CH = 0.8 * 10 = 8.

Answer: CH height is 8.