A surveyor standing 60 meters from the base of a tower measures the angle to the top of the tower and finds it to be 62.3degrees.  Use trigonometry to find the height of the tower.
62.3 degrees
60 m
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Part 1
The height of the tower is

enter your response here meters.

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.

A surveyor standing 60 meters from the base of a tower measures the angle to the top of the tower and finds it to be 62.3 degrees. Use trigonometry to find the height of the tower.

Learn how to use trigonometry to find the height of a tower based on a 62.3-degree angle of elevation and a 60-meter distance from the base. This step-by-step solution covers key trigonometric concepts and the tangent formula. Suitable for students in Grades 9-12.

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