**Find the height of a tower which casts a shadow 41 m long, when the angle of elevation of the sun is 36.50o.**

To find the height of the tower, we can use trigonometry, specifically the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (the height of the tower in this case) to the adjacent side (the length of the shadow).

Given:
- Length of the shadow (\( \text{adjacent side} \)) = 41 m
- Angle of elevation of the sun (\( \theta \)) = 36.50°

We can use the formula:

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

Rearranging to solve for the height of the tower:

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

Substituting the given values:

\[
\text{height of the tower} = \tan(36.50^\circ) \times 41 \, \text{m}
\]

Now, calculate the value:

\[
\tan(36.50^\circ) \approx 0.7385
\]

\[
\text{height of the tower} = 0.7385 \times 41 \, \text{m} \approx 30.279 \, \text{m}
\]

So, the height of the tower is approximately **30.28 meters**.

Would you like any further details or explanations? Here are some related questions:

1. How would the height change if the angle of elevation increased?
2. What would happen to the shadow length if the tower height doubled?
3. Can this method be used to calculate the height of a tree given its shadow?
4. What if the angle was 45°; how would that simplify the calculation?
5. How does the length of the shadow change throughout the day?

**Tip:** When solving trigonometric problems, always ensure your calculator is set to the correct unit (degrees or radians) as per the given angle.

Learn how to find the height of a tower casting a 41-meter shadow using trigonometry and the tangent function. Detailed step-by-step solution including the tangent formula application. Suitable for high school students studying trigonometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation