Question

Xavier uses a 20-foot ladder to paint a section of his house, and he rests it on a ledge that is 16 feet off the ground, as shown in the diagram. Solve for angle . Show your work.

Answer 1

The angle which ladder makes with the ground is 53.13

Explanation:

Given as :

The length of the ladder = 20 foot

The length of the ledge = 16 feet

The ladder makes an angle Ф with the ground

From figure, in triangle CAB

So, Sin angle =
`(\textrm Perpendicular)/(\textrm hypotenuse)`

I.e Sin Ф =
`(\textrm length of the ledge)/(\textrm length of the ladder)`

Or, Sin Ф =
`(16)/(20)`

or, Sin Ф =
`(4)/(5)`

or, Ф =
`Sin^(-1)((4)/(5))`

∴ Ф = 53.13

Hence The angle which ladder makes with the ground is 53.13 Answer