Question

Suppose a triangle has two sides of length 32 and 35, and that the angle between these two sides is 120 degrees. What is the length of the third side of the triangle?

Answer 1

cosine rule

`a^2=b^2+c^2-2bc*cos(A)`

`a^2=35^2+32^2-2*35*32*cos(120)`

`a^2=3369`
a is about 58.04

Answer 2

The length of the third side of the triangle is 58 units.

Explanation:

A triangle has two sides of length 32 and 35 and that the angle between these two sides is 120°

Using cosine law:

`c^2=a^2+b^2-2ab\cos C`

where,

a=32

b=35

∠C=120°

Substitute the value into formula and solve c

`c^2=32^2+35^2-2\cdor 32\cdot 35\cos120^\circ`

`c^2=3369`

`c=58.04\approx 58`

Hence, The length of the third side of the triangle is 58 units.