Question

The CN Tower The CN Tower, located in Toronto, Canada, is the tallest structure in the Americas. While visiting Toronto, a tourist wondered what the height of the tower above the top of the Sky Pod is. While standing 4000 feet from the tower, she measured the angle to the top of the Sky Pod to be 20.1°. At this same distance, the angle of elevation to the top of the tower was found to be 24.4°. Use this information to determine the height of the tower above the Sky Pod.

Short answer

The height above the sky pod on the CN tower is 350.8 feet.

Step-by-step solution

Step 1. Given information

The information given in the question is plotted in a diagram follows:

In this diagram we can see that the CN tower and the sky pod is given. Sky pod is at A and we need to find the distance AC and in the question it is given that:

$$\begin{gathered} BN=4000feet, \\ \angle ABN=20.1°, \\ \angle CBN=24.4°. \end{gathered}$$

Step 2. Trigonometric equations involved.

As we can see from the above diagram,

$$\begin{gathered} In∆ABNwehave, \\ \tan \left(20.1°\right)=\frac{AN}{BN}=\frac{AN}{4000}, \\ AN=4000\times \tan \left(20.1°\right)-------------\left(i\right) \\ And, \\ In∆CBNwehave, \\ \tan \left(24.4°\right)=\frac{CN}{BN}=\frac{AC+AN}{4000}, \\ AC+AN=4000\times \tan \left(24.4°\right), \\ AC=4000\times \tan \left(24.4°\right)-AN-------------\left(ii\right) \end{gathered}$$

Step 3. Solving equations to find the solution

$$\begin{gathered} From\left(i\right)and\left(ii\right)wehave, \\ AN=4000\times \tan \left(20.1°\right), \\ AC=4000\times \tan \left(24.4°\right)-AN. \\ PuttingthevalueofANinsecondweget, \\ AC=4000\times \tan \left(24.4°\right)-4000\times \tan \left(20.1°\right), \\ AC=4000(\tan \left(24.4°\right)-\tan \left(20.1°\right)), \\ AC=4000(0.4536-0.3659), \\ AC=4000(0.0877), \\ AC=350.8feet. \end{gathered}$$

So the height above the sky pod on the CN tower is 350.8 feet.