We are 330 feet from the base of a building. The angles of elevation to the top and bottom of a flagpole on top of the building are 55^(∘) and 53^(∘). We want to find the height x of the flapole. To do so, we will start by drawing a diagram of this situation.
Now, we will calculate the height h from the bottom of the building to the bottom the flagpole. From the diagram, we can see that the ground and the building form a right angle. Then, we can use the trigonometric ratio for tangent to find the height h.
tan θ = Opposite/AdjacentIn this case, the measure of the angle is 53^(∘), the length of the adjacent side is 330, and the length of the opposite side is h.
tan θ = Opposite/Adjacent ⇒ tan 53^(∘) = h/330
Let's solve this equation to obtain the value of h.
Next, we want to find the height H from the bottom of the building to the top of the flagpole. We will use again the trigonometric ratio for tangent. This time the measure of the angle is 55^(∘), the length of the adjacent side is 330, and the length of the opposite side is H.
tan 55^(∘) = H/330
We will solve this equation to obtain the value of H.
