Answer:
about 94.41°
Explanation:
The Law of Cosines can be used to find an angle in a triangle with three sides given.
Setup
The law of cosines relation generally relates the side opposite the angle to the other measures in the triangle:
r² = p² +q² -2pq·cos(R)
Solution
We want to find the measure of angle R, so we solve the equation for that:
2pq·cos(R) = p² +q² -r² . . . . . . add 2pq·cos(R)-r²
cos(R) = (p² +q² -r²)/(2pq) . . . . divide by the coefficient of the cosine
We can fill in the given side lengths at this point:
cos(R) = (13² +10² -17²)/(2·13·10) = -20/260 = -1/13
Then the angle can be found using the arccos function:
R = arccos(-1/13) ≈ 94.41°
The measure of angle R is about 94.41°.
__
Additional comment
When you have done a few of these, you recognize that the angle opposite side 'c' is ...
C = arccos((a² +b² -c²)/(2ab))
A calculator can make short work of this. The second attachment shows the evaluation of this expression with a=10, b=13, c=17. The calculator angle mode is set to degrees. The arccos function is the 2ND function of the Cos key.