To determine the height of the tree, we can use trigonometry. Specifically, the tangent function in a right triangle relates the angle of elevation, the height of the tree, and the distance from the observation point to the base of the tree:

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

Here:

• $\theta = 63^\circ$ is the angle of elevation.
• The opposite side is the height of the tree ($h$).
• The adjacent side is the distance from the observation point to the tree ($16 \, \text{ft}$).

Step 1: Use the formula

$\tan(63^\circ) = \frac{h}{16}$

Step 2: Solve for $h$

$h = 16 \cdot \tan(63^\circ)$

Step 3: Calculate $\tan(63^\circ)$

Using a calculator: $\tan(63^\circ) \approx 1.9626$

Step 4: Compute the height

$h = 16 \cdot 1.9626 = 31.40 \, \text{ft}$

Final Answer:

The height of the tree is approximately 31.40 feet.

---

Let me know if you need further clarification or details!

Related Questions:

1. How would the height of the tree change if the angle of elevation was larger?
2. How can we calculate the height if the distance from the observation point changes?
3. What tools can measure the angle of elevation accurately?
4. What other trigonometric functions could we use to solve similar problems?
5. How would we solve the problem if the tree were leaning?

Tip: Always ensure your angle measurements are in degrees (not radians) when performing trigonometric calculations unless otherwise stated.