The height of a right triangle divides the right angle into two angles, one of which is 40

The height of a right triangle divides the right angle into two angles, one of which is 40 degrees greater than the other. Find the sharp corners of this triangle.

In order to calculate the degree measures of acute angles ∠A and ∠B, it is necessary to calculate the degree measures ∠BCN and ∠AСН. Since one of them (∠ВСН) is larger than the other (∠АСН) by 40 degrees, we express:

x is the value of the angle ∠АСН;

x + 40 – the value of the angle ∠ВСН;

x + x + 40 = 90;

x + x = 90 – 40;

2x = 50;

x = 50/2 = 25;

∠АСН = 25º;

∠ВСН = 25 + 40 = 65º.

To calculate the degree measure of the angle ∠А, consider the triangle ΔАНС, which is rectangular with a right angle ∠АНС.

Since the sum of all the angles of the triangle is 180º, then:

∠А = 180º – ∠АСН – ∠АНС;

∠А = 180º – 25º – 90º = 65º.

To calculate the degree measure of the angle ∠В, consider the triangle ΔВНС, which is rectangular with a right angle ∠ВНС.

∠В = 180º – ∠ВСН – ∠ВНС;

∠В = 180º – 65º – 90º = 25º.

Answer: acute angle ∠A is equal to 65º, ∠B is equal to 25º.