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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 36º. 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.

2 Answers

7 votes

Final answer:

Using trigonometry with the tangent function, we calculated the height of the skyscraper above Sadie's eye level and then added her eye level height to find the total height. The skyscraper is approximately 198.97 meters tall.

Step-by-step explanation:

To determine the height of the skyscraper, we can use trigonometry. Sadie is standing 275 meters away from the skyscraper and measures an angle of elevation of 36º. We can use the tangent function, which is the ratio of the opposite side (the skyscraper's height above Sadie's eye level) to the adjacent side (the horizontal distance from Sadie to the skyscraper).

Tan(36º) = (Height of Skyscraper - Sadie's Eye Level) / Distance from Skyscraper

Let's denote the height of the skyscraper above Sadie's eye level as 'H'. Using the tangent function:

Tan(36º) = H / 275 m

Solving for 'H' gives us:

H = 275 m * Tan(36º)

H ≈ 197.28 meters

We add Sadie's eye level height to find the total height of the skyscraper:

Total Height of Skyscraper = H + Sadie's Eye Level

Total Height of Skyscraper ≈ 197.28 meters + 1.69 meters

Total Height of Skyscraper ≈ 198.97 meters

Therefore, the skyscraper is approximately 198.97 meters tall.

User C Taque
by
4.7k points
14 votes

Answer:I just got it wrong the answer is 201.49

Step-by-step explanation:

User Hesham Attia
by
4.3k points