Question

from her eye, which stands 1.75 meters above the ground, myesha measures the angle of elevation to the top of a prominent skyscraper to be 19°. if she is standing at a horizontal distance of 337 meters from the base of the skyscraper, what is the height of the skyscraper? round your answer to the nearest hundredth of a meter if necessary.

Explanation:

Step1: Identify the trigonometric relationship

We can use the tangent function in a right triangle, where $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 19^\circ$, the adjacent side is the horizontal distance (337 meters), and the opposite side is the height from Myesha's eye level to the top of the skyscraper, let's call it $h$. So $\tan(19^\circ)=\frac{h}{337}$.

Step2: Solve for $h$

Multiply both sides by 337: $h = 337\times\tan(19^\circ)$. Calculate $\tan(19^\circ)\approx0.3443$, then $h\approx337\times0.3443\approx116.03$.

Step3: Add Myesha's eye height

The total height of the skyscraper is $116.03 + 1.75 = 117.78$ meters.

Answer:

117.78 meters