The problem asks you to find the height of a tree given the angle of elevation and the distance from the point on the ground to the bottom of the tree.

From the diagram:

• The angle of elevation is 42°.
• The distance from the point on the ground to the bottom of the tree is 43 feet.

To solve this, we can use the tangent function from trigonometry. The formula is:

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

Where:

• $\theta = 42^\circ$,
• The opposite side is the height of the tree, which we are looking for (denote this as $h$),
• The adjacent side is the distance from the point on the ground to the bottom of the tree, which is 43 feet.

We can rearrange the formula to solve for the height of the tree:

$h = 43 \cdot \tan(42^\circ)$

Now, we can calculate the height:

$h = 43 \cdot \tan(42^\circ) \approx 43 \cdot 0.9004 \approx 38.7 \text{ feet}$

Thus, the height of the tree is approximately 38.7 feet.

Would you like more details or have any questions about the solution?

Here are five related questions you might find interesting:

1. How do you derive the tangent function from a right triangle?
2. How do you use other trigonometric functions like sine or cosine to solve similar problems?
3. What is the difference between angle of elevation and angle of depression?
4. How do you calculate distances in problems involving angles of elevation or depression?
5. How do you solve a problem involving a non-right triangle?

Tip: Always ensure your calculator is set to the correct mode (degrees or radians) before calculating trigonometric functions.