Question

A ladder leans against a brick wall. The foot of the ladder is 6 feet from the wall. The length of the ladder is 9 feet. Find to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground.

Answer 1

Explanation:

We can use trigonometry to solve this problem. Let's draw a right triangle to represent the situation:

|\

| \

h | \ 9 ft

| \

| \

| \

-------

6 ft

Here, h represents the height on the wall where the ladder touches. We want to find the angle of elevation θ.

Using the right triangle, we can write:

sin(θ) = h / 9

cos(θ) = 6 / 9 = 2 / 3

We can solve for h using the Pythagorean theorem:

h^2 + 6^2 = 9^2

h^2 = 9^2 - 6^2

h = √(9^2 - 6^2)

h = √45

h = 3√5

So, sin(θ) = 3√5 / 9 = √5 / 3. We can solve for θ by taking the inverse sine:

θ = sin^-1(√5 / 3)

θ ≈ 37.5 degrees

Therefore, to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground is 37.5 degrees.