Math question please help!?

Question

Ken is about to paint the front of a building. His ladder must reach a height of 9 m on the building, and the bottom is set 1.1 m from the base of the building. What is the angle, to the nearest tenth of a degree that the ladder makes with the ground? (Do not put degrees in your answer)

Answer 1

Draw the geometric diagram.

Observe, the above diagram.

Where, AB = ladder reaches the height on the building = 9 m.

BC =The distance between the ladder and the building = 1.1 m, and

AD =The height of the building.

Let, the angle that the ladder makes with the ground is x.

Using trigonometric identity : tan x = opposite/adjacent.

tan x = AB/BC.

Substitute corresponding values.

tan x = 9/(1.1) = 8.1818.

⇒ x = tan^{- 1} (8.1818)

       = 83.0 degrees 

        = 83 x (π/180)

        = 1.45 radians.

Therefore, the angle that the ladder makes with the ground is 1.45 radians.