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

Answer:

$7\sqrt{91}\ units$ or $66.78\ units$

Step-by-step 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

$c^{2}=42^{2}+35^{2}-2(42)(35)cos(120\°)$

$c^{2}=1,764+1,225-2,940cos(120\°)$

$c^{2}=4,459$

$c=\sqrt{4,459}\ units$

$c=7\sqrt{91}\ units$ or $c=66.78\ units$