Chapter 8.1, Problem 80AYU

One World Trade Center One World Trade Center (1WTC) is the centerpiece of the rebuilding of the World Trade Center in New York City. The tower is 1776 feet tall (including its spire). The angle of elevation from the base of an office building to the tip of the spire is $34°$. The angle of elevation from the helipad on the roof of the office building to the tip of the spire is $20°$.

(a) How far away is the office building from 1WTC? Assume the side of the tower is vertical. Round to the nearest foot.

(b) How tall is the office building? Round to the nearest foot.

To determine

To find:

a. How far away is the office building from 1 WTC? Assume the side of the tower is vertical. Round to the nearest foot.

Answer to Problem 80AYU

a. The office is about 2633 feet from the base of the tower.

Explanation of Solution

Given:

One World Trade Center (1WTC) is the centerpiece of the rebuilding of the World Trade Center in New York City. The tower is 1776 feet tall (including its spire). The angle of elevation from the base of an office building to the tip of the spire is $34°$. The angle of elevation from the helipad on the roof of the office building to the tip of the spire is $20°$.

Formula used:

$\text{tan}\theta =opp/adj$

Calculation:

Let $x$ be the distance between the buildings and let it be the adjacent side to the angle of elevation.

a. $\tan 34°=1776/x$

$x=\frac{1776}{\text{tan}34°}$

$x\approx 2633.03$

The office is about 2633 feet from the base of the tower.

To determine

To find:

b. How tall is the office building? Round to the nearest foot.

Answer to Problem 80AYU

b. Office building is 818 feet tall.

Explanation of Solution

Given:

One World Trade Center (1WTC) is the centerpiece of the rebuilding of the World Trade Center in New York City. The tower is 1776 feet tall (including its spire). The angle of elevation from the base of an office building to the tip of the spire is $34°$. The angle of elevation from the helipad on the roof of the office building to the tip of the spire is $20°$.

Formula used:

$\text{tan}\theta =opp/adj$

Calculation:

Let $x$ be the distance between the buildings and let it be the adjacent side to the angle of elevation.

b. $\text{tan}20°=\frac{y}{x}=y/2633$

$y=2633*\text{tan}20=958.33$

The Freedom tower is about 958 feet taller than the office building.

Office building is $1776-958=818$ feet tall.