Question

Two sides of a triangle are 13.9 cm and
24.2 cm, with the included angle 111
◦
.
What is the length of the third side?
Answer in units of cm

Answer 1

Considering 24.2 lies on x-axis and makes angle of 111 degree with side of triangle 13.9 cm long.
Therefore co-ordinate of the points of triangle are (24.2, 0)and (13.9 cos111 ,13.9 sin 111 )
Using distance formula third side is equal to square root of (24.2-13.9 cos111)^2+(0-13.9 sin 111)^2
=33.42

Answer 2

this is the way i know it probably there's shorter and easier way.

Answer 3

let's say "c" is the third side length, the other two "a" and "b".
and the angle between a and b is \[\gamma\]there is a formula tha gives c : \[c = \sqrt{a ^{2}+b^{2} - 2ab \cos \gamma}\]you can find it here http://en.wikipedia.org/wiki/Triangle

Answer 4

so \[c = \sqrt{13.9^{2} + 24.2^{2} - 2*13.9*24.2*\cos 111}\] c = 20.9558 cm