Step-by-step explanation:
The trigonometric function cosine is defined as the following:
[tex]cos(A) = \frac{adj}{hyp}[/tex]
where [tex]A[/tex] is any angle in a right triangle, [tex]adj[/tex] is the length of the side adjacent to angle [tex]A[/tex], and [tex]hyp[/tex] is the length of the hypotenuse of the triangle.
For this problem, we can fill in these values as follows:
[tex]cos(A) = \frac{10}{17}[/tex]
To solve for [tex]A[/tex], we need to take the inverse cosine of each side:
[tex]cos^{-1}(cos(A)) = cos^{-1}(\frac{10}{17})[/tex]
[tex]A = cos^{-1}(\frac{10}{17})[/tex]
Resolving this with a calculator results in [tex]53.986[/tex]°, or rounded to the nearest tenth, [tex]54.0[/tex]°
