Question

Ross is downtown Toronto and wants to determine how tall the CN Tower is (without using his smartphone). Ross stands 750m from the base of the tower and holds a clinometer at 1.5 m height and sights the tip of the tower at an angle of 36°. How tall is the CN Tower?
[4 marks]

Answer 1

Let $x$ mts be the height to the tip of the CN tower from the clinometer. Then $(x + 1.5)m$ is the height of the CN tower from the base. (Refer above figure.). Given, Ross stands 750m from the base and sights the tip of the tower at an angle $36^{\circ}$. Then, from the figure we get

$\tan 36^{\circ} = \dfrac{x}{750}\\ x=750*0.73 = 547.5~~~(\tan(36^{\circ}) \approx 0.73).$

Therefore, height of the CN tower from the base $\approx 547.5+1.5=549m.$