Question

question
from his eye, which stands 1.5 meters above the ground, moana measures the angle of elevation to the top of a prominent skyscraper to be 49°. if he is standing at a horizontal distance of 179 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.
answer
meters

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, $\theta = 49^\circ$, the adjacent side (horizontal distance) is 179 meters, and the opposite side is the height from Moussa's eye level to the top of the skyscraper, let's call it $h$. So $\tan(49^\circ)=\frac{h}{179}$.

Step2: Solve for $h$

Multiply both sides by 179: $h = 179\times\tan(49^\circ)$. Calculate $\tan(49^\circ)\approx1.1504$. Then $h\approx179\times1.1504 = 205.9216$.

Step3: Add the eye - level height

Moussa's eye is 1.5 meters above the ground, so the total height of the skyscraper $H=h + 1.5=205.9216+1.5 = 207.4216$.

Answer:

207.42 (rounded to the nearest hundredth)