Question

How do you work this out?

Answer 1

You can find x by using the pythagorean theorem:

`(2x+1)^2+(4x)^2 = (5x)^2`

`4x^2+4x+1+16x^2=25x^2`

`20x^2+4x+1 = 25x^2`

Bring everything to the same side:

`5x^2-4x-1=0`

The solutions to this equation are
`-(1)/(5)` and 1. We can't accept the negative solutions because it would lead to negative lengths, so we have
`x=1`

This implies that the triangle is a 3-4-5 triangle. Now, you can use the law of sines to state

`(5)/(\sin(90)) = (4)/(\sin(y)) \iff \sin(y) = (4)/(5) \iff y = \arcsin\left((4)/(5)\right)`