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

August 30, 2021 | education

| 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.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.