if the height of the tree is h, then if the angle is (x)

`h = 50tan(x)`

if the error in h is `Deltah` and the error corresponding in x is `Deltax`

`h+Deltah = 50tan(x+Deltax)`

if the percent error in h is 6%, `Deltah = 0.06h`

therefore,

`(h+Deltah)/h = (50tan(x+Deltax))/h`

...

## See

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

if the height of the tree is h, then if the angle is (x)

`h = 50tan(x)`

if the error in h is `Deltah` and the error corresponding in x is `Deltax`

`h+Deltah = 50tan(x+Deltax)`

if the percent error in h is 6%, `Deltah = 0.06h`

therefore,

`(h+Deltah)/h = (50tan(x+Deltax))/h`

`1.06 =(50tan(x+Deltax))/(50tan(x))`

but we know the angle is x = 71.5

therefore,

`tan(71.5+Deltax) = 1.06tan(71.5)`

`tan(71.5+Deltax) = 3.16800606`

`71.5+Deltax = 72.48`

`Deltax = 0.98`

`(Deltax)/(x) * 100 = 0.98/71.5 * 100 `

The percentage error that can happen in angle is = 1.37%