Anthony stands 40 meters from a
building that is 25 meters high. What is the angle of elevation from
Anthony to the top of the building? Round your answer to the nearest
Let’s begin by sketching the
problem. There is a building that is 25
meters high. Anthony is standing 40 meters
away. And we can assume that the ground
is horizontal and the building is vertical. So these two lines are
perpendicular to one another. We are asked to find the angle of
elevation from Anthony to the top of the building.
An angle of elevation is the angle
measured from the horizontal to the line of sight when we look up towards an
object. If we draw in the line of sight
from Anthony to the top of the building then, the angle we’re looking for is this
angle here. Let’s call that angle 𝜃.
Now, as we have a right triangle in
which we know two of the side lengths, we can approach this problem using right
triangle trigonometry. We’ll begin by labeling the sides
of this triangle, those whose lengths we know, in relation to this angle of 𝜃. The side of length 25 meters is the
opposite side, and the side of length 40 meters is the adjacent.
Recalling the acronym SOH CAH TOA
then, it is the tangent ratio that we need to use in this problem. This is defined as follows. For an angle 𝜃 in a right
triangle, tan of angle 𝜃 is equal to the length of the opposite side divided by the
length of the adjacent side. We know the lengths of these two
sides, and so we can form an equation. We have tan of 𝜃 is equal to 25
over 40. Now, this fraction can be
simplified by dividing both the numerator and denominator by five to give
To find the value of 𝜃, we need to
apply the inverse tangent function, giving 𝜃 is equal to the inverse tan of
five-eighths. We can now evaluate this on our
calculator, which must be in degree mode. It gives 32.005 continuing.
We’re asked to round our answer to
the nearest degree. So we’ll round this value to the
nearest integer, which is 32. By recalling then that an angle of
elevation is the angle formed between the horizontal and the line of sight when we
look up towards an object and then applying right triangle trigonometry, we found
that the angle of elevation from Anthony to the top of the building is 32 degrees to
the nearest degree.