To find the height of the skyscraper, we can use trigonometry. Specifically, we use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle.

The formula for tangent is:

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Variables:

• $\theta = 70^\circ$ (angle of elevation)
• Adjacent side = 276 m (horizontal distance)
• Opposite side = height of the skyscraper above Deondra's eye line ($h_{\text{above}}$)

Step 1: Solve for $h_{\text{above}}$

From the tangent formula: $h_{\text{above}} = \tan(70^\circ) \times 276$

First, calculate $\tan(70^\circ)$: $\tan(70^\circ) \approx 2.7475$

Now, calculate $h_{\text{above}}$: $h_{\text{above}} = 2.7475 \times 276 \approx 758.3 \, \text{m}$

Step 2: Add Deondra's height to find the total height

Deondra's eye is 1.66 m above the ground, so the total height of the skyscraper is: $h_{\text{total}} = h_{\text{above}} + 1.66$ $h_{\text{total}} = 758.3 + 1.66 = 759.96 \, \text{m}$

Final Answer:

The height of the skyscraper is approximately: $\boxed{760.0 \, \text{m}}$

Let me know if you'd like further clarification or details! 😊

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Expanding questions:

1. How would the height change if the angle of elevation were $60^\circ$?
2. What trigonometric identity relates tangent to sine and cosine?
3. How do you find the horizontal distance if the height and angle of elevation are given?
4. If Deondra stood at 150 m from the skyscraper, what would her angle of elevation be?
5. What role does precision in angle measurement play in this type of calculation?

Tip: Remember, in real-world scenarios, always account for measurement errors and ensure proper instrument calibration!