# 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 °.

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