Question

Find the missing variables

Answer 1

The triangle on the image is a right triangle which means we can use trigonometry to untangle its mysteries.

We have a side an and angle from that we can compute anything.

We will first compute x, we do so by taking the cosine of an angle,

`\cos(45)=(5√(2))/(x)`

`x=(5√(2))/(\cos(45))=(5√(2))/((√(2))/(2))=(10√(2))/(√(2))=\boxed{10}`

Then we can also compute y, simply by using pythagorean theorem,

`10^2=y^2+(5√(2))^2`

`y=\pm√(100-50)=\pm√(50)=\boxed{5√(2)}`.

So triangle has sides
`5√(2),5√(2),10` which is also known as equilateral triangle.

Hope this helps :)