In a right triangle, the bisector of the right angle divides the hypotenuse in the ratio of 3 is to 5. Determine the measures of the acute angles of the triangle.

Question

nurali · Answer

If you assume the portion of the hypotenuse with the 5 units is near the smaller angle of the right triangle, then drop a vertical line to the adjacent leg of the triangle, you will form a right triangle with a 5 units long hypotenuse.

A right triangle with a 5 unit long hypotenuse will have the opposite leg of 3 units and the adjacent leg of 4 units. There are only two numbers which make a right triangle when having a 5 unit hypotenuse. These are 3 and 4, with the 3 unit leg being the vertical leg of the right triangle.

Based on this, the sine of the smaller angle will be 3 / 5 which is 0.6
. 
The angle having a sine of 0.6 is 36.87 degrees. The other acute angle will be 90 - 36.87 = 53.13 degrees.

nurali · Answer

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