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The problem asks for the height of a vertical tower given that its shadow is 71.0 feet long and the angle of elevation of the sun is 29.0°.

This is a right triangle problem, where:
- The length of the shadow is the adjacent side of the triangle.
- The height of the tower is the opposite side of the triangle.
- The angle of elevation (29.0°) is the angle between the shadow and the line from the top of the tower to the sun.

Using trigonometry, specifically the tangent function:
\[
\tan(\theta) = \frac{{\text{opposite}}}{{\text{adjacent}}}
\]
In this case:
\[
\tan(29.0^\circ) = \frac{{\text{height of the tower}}}{{71.0 \, \text{ft}}}
\]

We can solve for the height of the tower:
\[
\text{height of the tower} = 71.0 \, \text{ft} \times \tan(29.0^\circ)
\]

Let me calculate that.The height of the tower is approximately **39.4 feet**, rounded to the nearest tenth.

Would you like further details or clarification on how this was solved?

Here are 5 related questions:
1. How do you convert degrees to radians in trigonometry?
2. What other trigonometric ratios could you use if different sides were given?
3. How would the solution change if the angle of elevation was increased?
4. What is the relationship between shadow length and angle of elevation?
5. Can you use the sine or cosine function to solve this problem, and how?

**Tip:** When solving problems involving right triangles, always identify which side corresponds to the opposite, adjacent, and hypotenuse based on the given angle to choose the correct trigonometric function.

The shadow of a vertical tower is 71.0 feet long when the angle of elevation of the sun is 29.0°. Find the height of the tower.

Learn how to calculate the height of a vertical tower given its shadow length of 71 feet and the angle of elevation of the sun (29.0°) using trigonometric functions. This right triangle problem is suitable for students in Grades 9-11 and covers key concepts in trigonometry.

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