Question

In an triangle, AC = BC and `AC^2 = 2AB^2`, then what will be angle of C?

Answer 1

`41.41^@`

Explanation:

Given `AC=BC, => DeltaABC` is isosceles.
Given `AC^2=2AB^2`,
`AC^2=AD^2+DC^2`
`AD=1/2AB, => AD^2=1/4AB^2`
`=> 2AB^2=1/4AB^2+DC^2`
`=> 7/4AB^2=DC^2, => DC=sqrt(7/4)AB=sqrt7/2AB`
`tanx=(AD)/(DC)=(1/2AB)/(sqrt7/2AB)`
`tanx=1/sqrt7`
`=> x=tan^-1(1/sqrt7)=20.705^@`

`=> angleACB=angleC=2x=2*20.705=41.41^@`