In this problem, a 7-meter tall tree casts a shadow that is 16 meters long, and we need to determine the angle at which the sun is positioned, using trigonometry.

This forms a right-angled triangle where:

• The height of the tree is the opposite side (7 m).
• The length of the shadow is the adjacent side (16 m).
• The angle of elevation of the sun (denoted as $\theta$) is the angle between the ground and the sun's rays.

To find the angle $\theta$, we use the tangent function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{7}{16}$

Now, let's calculate $\theta$ by finding the arctangent (inverse tangent) of this ratio.

Let me compute that for you.The angle at which the sun is positioned is approximately 24°.

Would you like further details or have any additional questions?

Here are some related questions:

1. What trigonometric ratios apply to right-angled triangles?
2. How would the angle change if the tree's height doubled but the shadow length remained the same?
3. Can we calculate the angle using sine or cosine instead of tangent in this scenario?
4. How does the angle of elevation of the sun vary throughout the day?
5. What would happen if the tree's height was less than the length of its shadow?

Tip: In right-angled triangles, the tangent function is especially useful when you know the opposite and adjacent sides.