Question

I need help It’s from my trigonometry prep book *It asks to round the answer to the nearest tenth of a degree

Answer 1

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}`