Question

1. the burj khalifa, located in dubai in the united arab emirates, is the tallest building in the world as of 2023. john visited dubai over winter break. he stood 1000 meters away from the building, looked up at a 38.5° angle using a laser rangefinder and spotted the top of the building.

a. how tall is the burj khalifa, in meters?
b. if every floor is 5.079 meters tall, how many floors are there in the burj khalifa?

Explanation:

Step1: Define tangent for height

Let $h$ = height of Burj Khalifa. Use $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan(38.62^\circ) = \frac{h}{1000}$

Step2: Solve for height $h$

Rearrange to isolate $h$.
$h = 1000 \times \tan(38.62^\circ)$
Calculate $\tan(38.62^\circ) \approx 0.800$, so $h \approx 1000 \times 0.800 = 800$ meters.

Step3: Calculate number of floors

Divide total height by floor height.
$\text{Number of floors} = \frac{800}{5.079}$

Step4: Compute floor count

Calculate the division, round to whole number.
$\text{Number of floors} \approx 157.5 \approx 158$

Answer:

a. 800 meters
b. 158 floors