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

Answer:

The angle which ladder makes with the ground is 53.13

Step-by-step 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 = $\dfrac{\textrm Perpendicular}{\textrm hypotenuse}$

I.e Sin Ф =  $\dfrac{\textrm length of the ledge}{\textrm length of the ladder}$

Or,  Sin Ф = $\frac{16}{20}$

or,   Sin Ф = $\frac{4}{5}$

or, Ф = $Sin^{-1}(\frac{4}{5})$

∴   Ф = 53.13

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