To find the height of the skyscraper, we can use trigonometry. The problem forms a right triangle where:

• The angle of elevation from Deondra’s eye to the top of the skyscraper is $70^\circ$.
• The horizontal distance from Deondra to the base of the skyscraper is 276 meters.
• Deondra’s eye level is 1.66 meters above the ground, which we need to account for.

We can use the tangent function from trigonometry, which relates the angle of elevation to the opposite side (height of the skyscraper above Deondra’s eye) and the adjacent side (horizontal distance).

Step 1: Set up the tangent equation

The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side:

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

Here:

• $\theta = 70^\circ$
• Opposite = $h_{\text{skyscraper}} - 1.66$ (because Deondra's eye is 1.66 meters above the ground)
• Adjacent = 276 meters

Thus, the equation becomes:

$\tan(70^\circ) = \frac{h_{\text{skyscraper}} - 1.66}{276}$

Step 2: Solve for $h_{\text{skyscraper}}$

$h_{\text{skyscraper}} - 1.66 = 276 \times \tan(70^\circ)$

$h_{\text{skyscraper}} - 1.66 = 276 \times 2.7475$

$h_{\text{skyscraper}} - 1.66 = 758.01$

Now, add 1.66 to both sides:

$h_{\text{skyscraper}} = 758.01 + 1.66$

$h_{\text{skyscraper}} = 759.67 \, \text{meters}$

Final Answer:

The height of the skyscraper is approximately 759.7 meters (rounded to the nearest tenth).

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Would you like more details on how the trigonometry works here? Or is there another concept you'd like to explore?

Here are 5 related questions:

1. How would the result change if the angle of elevation were smaller?
2. How do we solve this type of problem if the angle were given from the top of the building instead of the eye level?
3. What if we wanted to find the horizontal distance if the height and angle are given instead?
4. How do you solve a similar problem with an angle of depression?
5. How can you verify this solution using the Pythagorean theorem?

Tip: Always draw a diagram when solving trigonometric problems to visualize the situation more clearly!