Question

A 20-foot ladder is placed against a tree. The bottom is located 5 feet from the base of the tree and the top of the ladder is 5√15 feet up the tree. Use tangent to find the angle created between the ladder and tree. Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest tenth of a degree.

Answer 1

14.5°

Explanation:

The sketch results in an angle of depression problem.

In this case, the opposite side of the triangle formed is 5 ft

The hypotenuse side is 20 ft

The adjacent side is the
`5√(15)` ft

Using tangent θ = opp/adj

tangent θ = 5/
`5√(15)` =
`(1)/(√(15) )` = 0.258

θ =
`tangent^(-1)` 0.258 = 14.5°