1 Answer

Joe Ferndz · Answer 1 · 2023-03-02T17:04:22+0000

Given the hypotenuse of the right triangle:

$c=2\sqrt[]{15}cm$

And the shorter leg is:

$a=2\sqrt[]{6}cm$

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:

$\beta=\cos ^(-1)((adjacent)/(hypotenuse))$

Knowing the adjacent side and the hypotenuse, you can substitute them into the formula and evaluate:

$\beta=\cos ^(-1)(\frac{2\sqrt[]{6}}{2\sqrt[]{15}})$
$\beta\approx50.8\text{\degree}$

Hence, the answer is:

$\beta\approx50.8\text{\degree}$

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