To find the height of the tower, we can use the tangent function in trigonometry:

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

Where:

• $\theta = 36.50^\circ$ (angle of elevation)
• Length of the shadow = 41 m

Rearranging the formula to find the height of the tower:

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

Step 1: Calculate $\tan(36.50^\circ)$

Using a calculator: $\tan(36.50^\circ) \approx 0.7377$

Step 2: Substitute values into the formula

$\text{height of the tower} = 0.7377 \times 41$

$\text{height of the tower} \approx 30.34 \, \text{m}$

Final Answer:

30.34 m

Correct option:

(c) 30.34 m

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Related Questions:

1. What is the shadow length if the height of the tower is 50 m and the angle is 45°?
2. How does the angle of elevation affect the shadow length?
3. What is the formula for the tangent function in trigonometry?
4. If the angle of elevation is doubled, how does it impact the tower's shadow length?
5. How to compute the tangent value manually without a calculator?

Tip:

Always ensure your calculator is in degree mode when solving angle problems involving tr