Question

question
video examples
from her eye, which stands 1.74 meters above the ground, taub measures the angle of elevation to the top of a prominent skyscraper to be $51^\circ$. if she is standing at a horizontal distance of 148 meters from the base of the skyscraper, what is the height of the skyscraper? round your answer to the nearest tenth of a meter if necessary.
answer
attempt 1 out of 2
meters submit answer

Explanation:

Step1: Define unknown height segment

Let $x$ = height from eye level to skyscraper top.

Step2: Use tangent of elevation angle

$\tan(51^\circ) = \frac{x}{148}$
Rearrange to solve for $x$:
$x = 148 \times \tan(51^\circ)$
Calculate $\tan(51^\circ) \approx 1.2349$, so:
$x \approx 148 \times 1.2349 \approx 182.7652$

Step3: Add eye height to ground

Total height = $x + 1.74$
<Expression>
$182.7652 + 1.74 \approx 184.5052$

Step4: Round to nearest tenth

Round $184.5052$ to 1 decimal place.

Answer:

184.5 meters