This problem involves right triangle trigonometry. We can use the tangent function because we have the opposite side (height of the tree) and the adjacent side (shadow length).

Given:

• Shadow length = 25 meters
• Angle of elevation = 30°
• Let h be the height of the tree.

Using the tangent function:

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

$\tan(30^\circ) = \frac{h}{25}$

From trigonometric values:

$\tan(30^\circ) = \frac{1}{\sqrt{3}}$

$\frac{1}{\sqrt{3}} = \frac{h}{25}$

Solving for h:

$h = 25 \times \frac{1}{\sqrt{3}}$

$h = \frac{25}{\sqrt{3}}$

To rationalize the denominator:

$h = \frac{25\sqrt{3}}{3}$

Approximating:

$h \approx \frac{25 \times 1.732}{3}$

$h \approx \frac{43.3}{3}$

$h \approx 14.43 \text{ meters}$

Final Answer:

The tree is approximately 14.43 meters tall.

Would you like more details on any step? Here are some related questions:

1. How do you derive the tangent function in right triangles?
2. What are the trigonometric ratios of 30°, 45°, and 60°?
3. How do you rationalize a denominator with a square root?
4. How do you find the height of an object using a clinometer?
5. How does changing the angle of elevation affect shadow length?

Tip: Always check if your calculator is set to degrees when solving trigonometric problems!