Question

A 4-m plank rests against a wall 1.8 m high so that 1.2 m of its projects beyond the wall. Find the angle the plank makes with the wall.
this is a trigonometry word problem. please solve after drawing what is said so I can understand.

Answer 1

Answer:

50.0°

Explanation:

In the diagram below, line AD represents the plank and line BC represents the wall.

θ is the angle the plank makes with the wall.

Length of the plank on the wall

The plank is 4 m long and 1.2 m extends beyond the wall.

The length of the plank resting on the wall is

AB = 4 – 1.2

AB = 2.8 m

===============

Angle with the wall

Triangle ABC is a right triangle, because the wall is perpendicular to the ground.

cosθ = BC/AB

BC = 1.8 m; AB = 2.8

cosθ = 1.8/2.8

θ = cos⁻¹(1.8/2.8)

θ = cos⁻¹(0.6429)

θ = 50.0°

The plank makes an angle of 50.0° with the wall.