To find the angle of elevation, we can use the tangent function from trigonometry:

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

where:

• opposite = 168 feet (height of the tree),
• adjacent = 58 feet (horizontal distance from the base of the tree),
• $\theta$ is the angle of elevation.

Step 1: Use the tangent function

$\tan(\theta) = \frac{168}{58}$

Step 2: Compute the value

$\tan(\theta) = 2.8966$

Step 3: Take the arctangent (inverse tangent)

$\theta = \tan^{-1}(2.8966)$

Using a calculator:

$\theta \approx 70.9^\circ$

Final Answer:

$\boxed{70.9^\circ}$

Would you like a step-by-step explanation of how to use a calculator for this?

Related Questions:

1. How would the angle change if the observer was farther away?
2. What if the tree was only 100 feet tall but at the same distance?
3. How can the sine or cosine function be used in this scenario?
4. What if the observer was standing on a hill instead of level ground?
5. How can this concept be applied in real-life situations like construction or navigation?

Tip:

Always check that your calculator is in degree mode when solving angle problems!