Answer to Question #111976 in Trigonometry for Blake Petsinis

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 $\approx 547.5+1.5=549m.$