Find the length of the third side of a triangle if the area of the triangle is 18 and two of its sides have lengths of 5 and 10.

Answer 1

Let the angle between the 2 given sides by Ø

then
(1/2)(5)(10)sinØ = 18
sinØ = 18/25

by Pythagoras: cosØ = √301/25

let the third side be x
by the Cosine Law

x^2 = 5^2 + 10^2 - 2(5)(10)cosØ
= 125 - 100(√301/25)
= 55.60259...
x = appr 7.46