A superhero is running toward a skyscraper to stop a villain from getting away. As he is moving, he looks up at the top of the building and his line of sight makes a 33.0° angle with the ground. After having moved 350 m, he looks at the top of the building again, and notices that his line of sight makes a 52.0° angle with the horizontal. How tall is the skyscraper?
+129842 Let m be the total distance he is from the skyscraper when he first sights it...and let h be the height of the skyscraper......so we have.....
tan (33) = h/m → m = h/tan (33)
After he runs 350m....he is (m - 350)m from the skyscraper
And we have that
tan (52) = h / [ m - 350] substitute for m to get an equation in one variable
tan (52) = h / [ h/tan (33) - 350] multiply both sides by [ h/tan (33) - 350]
[ h/tan (33) - 350] * tan (52) = h simplify
h [ tan(52)/tan(33) ] - 350 * tan(52) = h rearrange and factor
h [ tan (52) / tan(33) - 1 ] = 350 * tan(52) divide both sides by [ tan (52) / tan(33) - 1 ]
h = 350 * tan(52) / [ tan (52) / tan(33) - 1 ] ≈ about 461.39 m
