Note that in any right triangle, the tangent of an acute angle is the opposite side divided by the adjacent side.
From the problem, we have a missing side that can be obtain using the Pythagorean Theorem.
[tex]c^2=a^2+b^2[/tex]
where c is the hypotenuse, a and b are the legs of the triangle.
So we have, c = 17 and a = 8
[tex]\begin{gathered} 17^2=8^2+b^2 \\ 289=64+b^2 \\ 289-64=b^2 \\ 225=b^2 \\ b=\sqrt[]{225} \\ b=15 \end{gathered}[/tex]
Now we have the side 15.
In a right triangle, there are two accute angles.
The lower left and the upper right.
For the lower left angle, the opposite side is 8 and the adjacent side is 15.
So the tangent of this angle is 8/15
For the upper right angle, the opposite side is 15 and the adjacent side is 8.
So the tangent of this angle is 15/8
ANSWER :
8/15 and 15/8
