Video: Finding the Angle of Elevation

Jess stands 40 m from a building 25 m high. What is the angle of elevation from Jess to the top of the building?


Video Transcript

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.

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