Question

A ladder 35 feet in length rests against a vertical wall. The foot of the ladder is 10 feet from the wall. What angle, θ, does the ladder make with the ground?

Which of the following equations can be used to solve the problem?

cosθ = 10/35
sinθ = 10/35
tanθ = 10/35

Answer 1

cos(theta)= 10/35
This is because the cos is equal to the adjacent side over the hypotenuse, and both of these values are given to you (adjacent side= 10 feet and hypotenuse=35 feet).

Answer 2

The equation that can be used to solve the problem is: cos θ =
`(10)/(35)`

and the angle the ladder make with the wall is θ=73.4°

Explanation:

To solve the problem, we are going to use the trigonometric formula;

SOH CAH TOA

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

From the diagram below, hypotenuse is given to be equal to 35 feet, adjacent is given to be equal 10 feet, to find angle θ, the best formula to use is;

cos θ= adjacent / hypotenuse

where hypotenuse=35 feet and adjacent = 10 feet

We can now proceed to insert our values into the formula;

cos θ =
`(10)/(35)`

cos θ = 0.28571

To find the value of θ, we will need to take the
`cos^(-1)` of both-side

`cos^(-1)`cos θ =
`cos^(-1)`0.28571

θ=73.4°

Therefore, the angle the ladder make with the wall is θ=73.4°