If the angle of elevation of the sun is 74.3° when a building casts a shadow of 61.3 feet, what is the height of the building, in feet? Round your answer to the correct number of significant digits.

To find the height of the building, we can use basic trigonometry. Since the angle of elevation forms a right triangle with the building and its shadow, the tangent of the angle of elevation is the ratio of the height of the building to the length of the shadow.

The formula is:

\[
\tan(\theta) = \frac{{\text{{height}}}}{{\text{{shadow length}}}}
\]

Where:
- \(\theta = 74.3^\circ\)
- \(\text{{shadow length}} = 61.3 \, \text{{feet}}\)
- \(\text{{height}} = ?\)

Solving for height:

\[
\text{{height}} = \tan(\theta) \times \text{{shadow length}}
\]

Now, let's calculate the height.The height of the building is approximately 218 feet, rounded to three significant digits.

Do you want more details or have any further questions?

Here are some related questions you might find helpful:
1. How do you calculate the angle of elevation if the height and shadow length are known?
2. What is the role of trigonometric functions in solving right triangles?
3. How can you solve for the shadow length if the height and angle are given?
4. What are some real-world applications of angle of elevation problems?
5. How do you estimate measurement uncertainty in trigonometric calculations?

**Tip:** When dealing with right triangles, always check if the problem involves sine, cosine, or tangent based on the sides and angles given.

Solve a trigonometric problem where the angle of elevation of the sun is 74.3° and the shadow length is 61.3 feet. Learn how to calculate the height of the building using the formula tan(θ) = height / shadow length. This problem covers trigonometry concepts and is suitable for students in Grades 9-11.

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