Answer :
The height of the skyscraper is approximately 198.36 meters.
To find the height of the skyscraper, we can use trigonometry. We have a right triangle formed by the observer (her eye), the top of the skyscraper, and the base of the skyscraper (the ground).
Given:
- The angle of elevation from her eye to the top of the skyscraper is 36°.
- The horizontal distance from her eye to the base of the skyscraper is 275 m.
- The height of her eye above the ground is 1.69 m.
We can use the tangent function, which relates the angle of elevation [tex](\( \theta \))[/tex] to the opposite side (height of the skyscraper, ( h ) and the adjacent side (horizontal distance, ( d ):
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
Substituting the given values:
[tex]\[ \tan(36^\circ) = \frac{h + 1.69}{275} \][/tex]
Now, we solve for ( h ):
[tex]\[ h + 1.69 = 275 \times \tan(36^\circ) \][/tex]
[tex]\[ h = 275 \times \tan(36^\circ) - 1.69 \][/tex]
Let's calculate ( h ):
[tex]\[ h = 275 \times \tan(36^\circ) - 1.69 \][/tex]
[tex]\[ h \approx 275 \times 0.726542528 - 1.69 \][/tex]
[tex]\[ h \approx 200.0496948 - 1.69 \][/tex]
[tex]\[ h \approx 198.3596948 \][/tex]
Therefore, the height of the skyscraper is approximately 198.36 meters.
