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

The height of a right-angled triangle divides the right angle into two angles, one of which is 40 degrees larger than the other, find the sharp corners of the triangle.

Let the smaller angle, which is obtained by dividing the height of the right angle, will be equal to the variable a.

Then the larger angle that is obtained by dividing the height of the right angle can be written as a + 40.

Since we know that in total they are equal to 90 °, then it is possible to write down the equation and find out the magnitude of each of them:

a + a + 40 = 90;

2a = 50;

a = 25;

25 + 40 = 65.

Let’s determine what the first acute angle of our triangle will equal:

90 – 25 = 65.

Then the second one:

90 – 65 – 25.

Answer: The angles are 25 ° and 65 °.