Chapter 8.1, Problem 72AYU

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.

To determine

The height of the tower above the Sky Pod.

Answer to Problem 72AYU

The height of the tower above the Sky Pod is $350.69$ feet.

Explanation of Solution

Given:

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 $24.4°$.

Formula used:

$\text{tan}A=\frac{\text{opp side}}{\text{base}}$

Calculation:

Let $h$ be the height of the balloon.

$\text{tan}20.1°=\frac{b}{4000}$

$b=4000*\text{ tan}20.1$

$b=1463.79$

$\tan 24.4°=\frac{h+b}{4000}$

$h+b=4000*\text{ tan}24.4°$

$h\approx 1814.48°-1463.79°$

$h=350.69$

The height of the tower above the Sky Pod is $350.69$ feet.