Jess stands 40 metres from a
building 25 metres high. What is the angle of elevation
from Jess to the top of the building?
So, as I suggested before, a
diagram would be a really good place to start with this question. So, this time, I’ve just
represented Jess by a dot. We haven’t been told anything
about her height. So, we’re not taking that into
account. She’s 40 metres from the
building, which is 25 metres high. And we are making the
reasonable assumption here that the building is at a right angle to the floor,
which is horizontal. So, we’re looking to calculate
the angle of elevation as Jess looks up at the top of the building. So, it’s this angle that I’ve
marked as 𝜃 on the diagram.
So, as before, it’s a
trigonometry problem, so always sensible to label the three sides of the
triangle first. So, the hypotenuse, the longest
side here, the opposite which is the side opposite that angle 𝜃, and then the
adjacent which is between 𝜃 and the right angle. The two sides we’ve been given
are the opposite and the adjacent. So, we’re going to be using
that tangent ratio again. So, let’s write down its
definition. So, tan of 𝜃 is equal to the
opposite divided by the adjacent.
So, what I’m gonna do is I’m
gonna write this ratio down. But I’m gonna replace the
opposite and the adjacent with their values in this question, so 25 and 40. So, I have tan of 𝜃 is equal
to 25 over 40. Now, that does actually
simplify as I can divide both parts of this ratio through by five. So, if I wanted to, I could
simplify it to five over eight. Now, as we’re looking to
calculate an angle this time rather than a side, we need to use that inverse tan
function in order to do this.
So, I have that 𝜃 is equal to
tan inverse of five over eight. And at this point, I’m gonna
reach for my calculator to evaluate that. So, this tells me that 𝜃 is
equal to 32.00538. And if I round that to the
nearest degree then, I have my answer to this question, which is that the angle
of elevation is 32 degrees. So, as before, start with a
diagram, identify the sides of the right-angled triangle, and then use the tan
ratio in order to find this missing angle.