Question

How to find the missing length of an obtuse triangle if two sides have a length of 10 one of the angles is 120 degrees?

Answer 1

The length is `10sqrt(3)`

To calculate we can use the law of cosines:

if we denote the equal sides of the triangle as `a`, and the missing one as `b`, we can write:

`b^2=a^2+a^2-2a^2cos120`
`b^2=2a^2-2a^2cos120`
`b^2=2a^2(1-cos120)`
`b^2=2*10^2(1-cos120)`
`b^2=200(1-cos(90+30))`
`b^2=200(1+sin30)`
`b^2=200(1+1/2)`
`b^2=300`
`b=sqrt(300)=10sqrt(3)`