Question

1. the burj khalifa, located in dubai in the united arab emirates, is the tallest building in the world as of 2022. andre visited dubai over winter break. he stood 700 meters away from the building, looked up at a 48.11 degree 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 5.032 meters tall, how many floors are there in the burj khalifa?

Explanation:

Step1: Define tangent for height

Let $h$ = height of Burj Khalifa. Use $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$, where $\theta=48.11^\circ$, adjacent = 700 m.
$\tan(48.11^\circ) = \frac{h}{700}$

Step2: Calculate building height

Rearrange to solve for $h$.
$h = 700 \times \tan(48.11^\circ)$
$\tan(48.11^\circ) \approx 1.119$, so $h \approx 700 \times 1.119 = 783.3$ meters

Step3: Calculate number of floors

Divide total height by floor height (5.032 m).
$\text{Number of floors} = \frac{783.3}{5.032}$

Step4: Round to whole number

Floors are whole units, so round to nearest integer.
$\frac{783.3}{5.032} \approx 155.66 \approx 156$

Answer:

a. 783.3 meters
b. 156 floors