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To solve this problem, we need to use basic trigonometry. The surveyor forms a right triangle with the tower. Here's the information we have:

- The distance from the base of the tower (adjacent side) is 85 meters.
- The angle of elevation to the top of the tower is 61.9°.
- We are solving for the height of the tower (opposite side).

Using the tangent function, which relates the opposite and adjacent sides in a right triangle:

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

Substituting the known values:

\[
\tan(61.9^\circ) = \frac{h}{85}
\]

Where \( h \) is the height of the tower.

Now, solving for \( h \):

\[
h = 85 \times \tan(61.9^\circ)
\]

I will calculate this next.The height of the tower is approximately **159.19 meters**.

Would you like any further details or clarifications?

Here are 5 related questions to expand your understanding:
1. How would the height change if the angle of elevation were smaller?
2. What trigonometric function would you use if you were given the height and wanted to find the distance from the base?
3. How can you apply the sine or cosine functions in similar right-triangle problems?
4. What if the distance from the base was unknown? How could you find it using trigonometry?
5. How would this problem change if the tower was on a hill, and the ground wasn’t flat?

**Tip:** Always check the units of the given values to ensure consistency in trigonometry problems.

A surveyor standing 85 meters from the base of a tower measures the angle to the top of the tower and finds it to be 61.9°. Use trigonometry to find the height of the tower.

Learn how to calculate the height of a tower using the tangent function. A surveyor stands 85 meters away from the base of the tower and measures an angle of elevation of 61.9°. This problem explains key trigonometric concepts, including the use of right triangles and tangent functions. Suitable for students in Grades 9-11.

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