Estimating the Height of a Building

Consider the problem of calculating the height of a building. As a student stands outside the building, she wonders how she will accomplish such a task without a really long tape measure! She then remembers she has a protractor and performs the following calculations:

She notes that, at a distance of 10 feet from the building, the angle of elevation is 75°. This is all the information she needs to estimate the height of the building. How will she accomplish this?

She draws the following figure:

Then she notes that, since , she can solve for y as This leaves her with just one job: calculating . She can calculate this using the sum formula for .

Therefore, she knows that or 37.3205 feet.