Explanation:
remember the law of cosine :
c² = a² + b² - 2ab×cos(C)
a, b, c being the sides of the triangle, C being the angle opposite of line c.
this applies to all angles and their opposite sides, we only need to adapt what sides we use at what position in the formula.
so, in our example we need to find E.
the opposite side of E is 12.
so, the formula is
12² = 10² + 13² - 2×10×13×cos(E)
144 = 100 + 169 - 260×cos(E)
-125 = -260×cos(E)
cos(E) = -125/-260 = 25/52 = 0.480769231...
angle E = 61.26434626...° ≈ 61°