Given the hypotenuse of the right triangle:
[tex]c=2\sqrt[]{15}cm[/tex]
And the shorter leg is:
[tex]a=2\sqrt[]{6}cm[/tex]
You can draw the Right Triangle. See the image below (it is not drawn to scale):
Let be β the measure (in degrees) of the larger acute angle of the right triangle.
In order to find β, you can apply the following Inverse Trigonometric Function:
[tex]\beta=\cos ^{-1}(\frac{adjacent}{hypotenuse})[/tex]
Knowing the adjacent side and the hypotenuse, you can substitute them into the formula and evaluate:
[tex]\beta=\cos ^{-1}(\frac{2\sqrt[]{6}}{2\sqrt[]{15}})[/tex][tex]\beta\approx50.8\text{\degree}[/tex]
Hence, the answer is:
[tex]\beta\approx50.8\text{\degree}[/tex]
