To solve for the height of the tree, we can use trigonometry. Specifically, we can use the tangent of the angle of elevation.

Steps:

1. Let $h$ be the height of the tree (what we're solving for).
2. The angle of elevation is given as 50°.
3. The length of the shadow is 38 feet.

We can set up the equation using the tangent function, which is defined as:

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

Here, the opposite side is the height of the tree $h$, and the adjacent side is the length of the shadow, which is 38 feet.

$\tan(50^\circ) = \frac{h}{38}$

Solve for $h$:

$h = 38 \times \tan(50^\circ)$

Using a calculator:

$h = 38 \times 1.1918 \approx 45.3$

Final Answer:

The height of the tree is approximately 45 feet (rounded to the nearest foot).

Would you like a more detailed explanation of the steps or have any other questions? Here are some related questions you might find helpful:

1. How do you use the sine or cosine function in similar problems?
2. What is the difference between the tangent and sine functions in trigonometry?
3. How do you calculate the shadow length if the height of the tree and angle of elevation are known?
4. What is the relationship between the angle of elevation and the height of an object?
5. How can we solve for angles in right triangles using trigonometric ratios?

Tip: Always check if your calculator is in degrees or radians before performing trigonometric calculations!