Question

question
from her eye, which stands 1.69 meters above the ground, sadie measures the angle of elevation to the top of a prominent skyscraper to be 36°. if she is standing at a horizontal distance of 275 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.
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attempt 1 out of 2
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Explanation:

Step1: Use the tangent function

The tangent of an angle of elevation in a right - triangle is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Let \(h\) be the height from Sadie's eye level to the top of the skyscraper. We know \(\theta = 36^{\circ}\) and the adjacent side \(x = 275\) meters. So, \(\tan(36^{\circ})=\frac{h}{275}\).

Step2: Solve for \(h\)

We can rewrite the equation as \(h = 275\times\tan(36^{\circ})\). Using a calculator, \(\tan(36^{\circ})\approx0.7265\). Then \(h=275\times0.7265 = 275\times\frac{7265}{10000}=275\times\frac{1453}{2000}=\frac{275\times1453}{2000}=\frac{400575}{2000}=200.2875\) meters.

Step3: Add Sadie's height above the ground

The total height \(H\) of the skyscraper is \(H=h + 1.69\). Substitute \(h = 200.2875\) into the equation: \(H=200.2875+1.69=201.9775\approx201.98\) meters.

Answer:

\(201.98\) meters