Question

suppose a triangle has two sides of length 42 and 35 and that the angle.between these two sides is 120° what is the length of the third side of the triangle

Answer 1

Answer:

The length of the third side of the triangle is $7\sqrt{91}\ units$

Step-by-step explanation:

Let

c ----> the length of the third side of the triangle

we know that

Applying the law of cosines

$c^2=a^2+b^2-2(a)(b)cos(C)$

we have

$a=42\ units\\b=35\ units\\C=120^o$

substitute the given values

$c^2=42^2+35^2-2(42)(35)cos(120^o)$

$c^2=2,989-2,940cos(120^o)$

$c^2=4,459\\c=\sqrt{4,459}\ units\\c=7\sqrt{91}\ units$