To find the height of the tower, we can use trigonometry. Specifically, we can apply the tangent function, which relates the angle of elevation to the opposite side (height of the tower) and the adjacent side (distance from the base).

The formula is:

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

Where:

• $\theta = 62.3^\circ$ (the angle of elevation)
• Opposite = height of the tower (let's call it $h$)
• Adjacent = 60 meters (distance from the base)

Rearranging the equation to solve for $h$:

$h = \tan(62.3^\circ) \times 60$

Now, we calculate the tangent of $62.3^\circ$ and solve for $h$.The height of the tower is approximately 114.28 meters.

Do you have any questions, or would you like more details on the calculation?

Here are some related questions to explore:

1. How would the height change if the angle were 45 degrees?
2. What if the surveyor stood 100 meters away instead of 60 meters?
3. How would you use the sine or cosine function in this scenario?
4. What if the tower had an incline at the top? How would that affect the angle measurement?
5. Can this method be used for finding the height of a mountain? Why or why not?

Tip: When using trigonometric functions, make sure your calculator is set to the correct mode (degrees or radians) based on the angle you're working with.