Tangent Ratios: Determine the height of the CN Tower to the nearest metre.

Question

While standing a certain distance across flat ground from the base of the CN tower, Raj notices that the angle of elevation to the top of the CN Tower is 41.3∘. He then walks 180 metres toward the CN Tower and notices that the angle of elevation to the top of the tower has increased to 50.9∘. Determine the height of the CN Tower to the nearest metre.

(Trigonometry unit: Tangent Ratios)

Answer 1

I will set this up for you, but YOU do the math. Draw a picture of the situation described in the problem. Let x be the distance from the CN tower to where the angle was measured to be 50.9°, and let h be the height of the CN tower. Note that

h/x = tan50.9°

h/(x + 180) = tan41.3°

You now have a system of 2 equations in 2 unknowns h and x. Solve the system (probably easiest by substitution) and get h in meters.