# The height to the hypotenuse is drawn in a right-angled triangle.

**The height to the hypotenuse is drawn in a right-angled triangle. What angles does this height form with the legs if the larger of the acute angles of this triangle is 79 °?**

Given:

right-angled triangle ABC;

angle C = 90 °;

CH is the height drawn to the hypotenuse;

angle B = 79 °.

Find the degree measures of the angle АСН and the angle ВСН -?

Solution:

1) Consider the СВН triangle. We know that the sum of the degree measures of any triangle is 180 degrees. Hence:

angle НСВ = 180 ° – angle СНВ – angle НВС;

angle НСВ = 180 ° – 90 ° – 79 °;

angle НСВ = 90 ° – 79 °;

angle НСВ = 11 °;

2) Consider the triangle ACB.

Angle A = 180 ° – 90 ° – 79 °;

Angle A = 11 °;

3) Consider the ASN triangle.

Angle АСН = 180 ° – 90 ° -11 °;

Angle ACН = 90 ° -11 °;

Angle ACН = 79 °.

Answer: 79 °; 11 °.