The shadow of a vertical tower is 72.0 ft long when the angle of elevation of the sun is 30.0 degrees. Find the height of the tower.
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Part 1
The tower is 
  
enter your response here ft tall.
​(Simplify your answer. Type an integer or decimal rounded to the nearest tenth as​ needed.)

To find the height of the tower, we can use trigonometry. The situation involves a right triangle where:

- The height of the tower (\( h \)) is the opposite side of the angle.
- The shadow of the tower (72.0 ft) is the adjacent side.
- The angle of elevation of the sun is 30.0 degrees.

We can use the tangent function, which relates the angle to the opposite and adjacent sides in a right triangle:

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

Substituting the known values:

\[
\tan(30^\circ) = \frac{h}{72.0}
\]

Now, solve for \( h \):

\[
h = 72.0 \times \tan(30^\circ)
\]

The tangent of 30 degrees is \( \frac{1}{\sqrt{3}} \) or approximately 0.577. Thus:

\[
h = 72.0 \times 0.577 = 41.6 \text{ ft}
\]

So, the height of the tower is **41.6 ft**.

Would you like more details or explanations?

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Here are 5 related questions for practice:
1. What is the length of the shadow when the angle of elevation is 45 degrees and the height is 50 ft?
2. How does the angle of elevation change if the shadow becomes shorter?
3. If the height of the tower was doubled, what would the new shadow length be for the same angle of elevation?
4. What trigonometric function would you use if the angle of elevation and the height of the tower were given, but you needed to find the shadow length?
5. How would the height change if the angle of elevation increased to 60 degrees but the shadow length remained the same?

**Tip:** In trigonometry problems involving angles of elevation, drawing the right triangle can help visualize the situation and select the correct function.

The shadow of a vertical tower is 72.0 ft long when the angle of elevation of the sun is 30.0 degrees. Find the height of the tower.

Learn how to calculate the height of a tower given that the shadow is 72.0 ft long and the angle of elevation of the sun is 30 degrees. This problem uses the tangent function and is suitable for students in Grades 9-11.

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