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

The length of third side of the triangle is:

66.78 units.

Explanation:

We are given one side of a triangle let 'a': 42 units.

Also the other side of the triangle let 'b': 35 units.

Also, the angle between the two sides let C=120 degree.

Also we know that the cosine rule to find the third side( let 'c') is given by:

`c^2=a^2+b^2-2ab\cos C\\\\c^2=(42)^2+(35)^2-2* 42* 35* \cos (120\degree)\\\\c^2=1764+1225+1470`

Since,

`\cos (120)=\cos (90+30)\\\\\cos (120)=-\sin (30)\\\\\cos (120)=-(1)/(2)`

Hence,

`c^2=4459\\\\c=√(4459)\\\\c=66.7757`

which is approximately equal to:

66.78 units.

Hence, length of third side of the triangle is:

66.78 units