Two legs of a right triangle have 11 and 13 what is the measure of the larger acute angle?
To find the measure of the larger acute angle of a right triangle, we can use trigonometric ratios. In this case, we can use the tangent ratio.
The tangent of an acute angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this triangle, the side opposite the larger acute angle has a length of 11, and the side adjacent to the larger acute angle has a length of 13.
So, the tangent of the larger acute angle can be calculated as follows:
tan(angle) = opposite/adjacent = 11/13
To find the measure of the angle itself, we need to take the arctangent (or inverse tangent) of this value using a calculator:
angle = arctan(11/13)
Using a calculator, we find that arctan(11/13) is approximately 43.96 degrees.
Therefore, the measure of the larger acute angle is approximately 43.96 degrees.