To determine the height of the tree, we can use trigonometry. Specifically, we can apply the tangent function, which is defined in a right triangle as:

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

Where:

• $\theta = 49^\circ$ (the angle of elevation),
• The opposite side is the height of the tree (which we are solving for),
• The adjacent side is the horizontal distance from the point on the ground to the bottom of the tree (53 feet).

Let $h$ represent the height of the tree. The equation becomes:

$\tan(49^\circ) = \frac{h}{53}$

Now, solve for $h$:

$h = 53 \times \tan(49^\circ)$

Using a calculator:

$h = 53 \times 1.1504 \approx 60.97$

So, the height of the tree is approximately 60.97 feet.

Would you like more details or have any questions about this process? Here are some related questions for further exploration:

1. How would the height change if the angle of elevation were increased to 60 degrees?
2. What happens if the horizontal distance is increased to 100 feet?
3. Can we apply other trigonometric functions to solve this kind of problem?
4. How does the height of the tree relate to the sine and cosine functions?
5. How would the solution change if the angle of elevation were measured from the top of the tree instead of the ground?

Tip: Remember that when using trigonometric functions, the angle must always be in the correct unit (degrees or radians), depending on your calculator settings.