Question

Suppose a triangle has to size of lint 42 and 35 and the angles between these 2 sides is 120 which equated should you solve to find the length of the 3rd side of a triangle

Answer 1

`7√(91)\ units` or
`66.78\ units`

Explanation:

we know that

Applying the law of cosines

`c^(2)=a^(2)+b^(2)-2abcos(C)`

In this problem we have

`a=42\ units, b=35\ units, C=120\°`

c is the length of the third side

Substitute

`c^(2)=42^(2)+35^(2)-2(42)(35)cos(120\°)`

`c^(2)=1,764+1,225-2,940cos(120\°)`

`c^(2)=4,459`

`c=√(4,459)\ units`

`c=7√(91)\ units` or
`c=66.78\ units`