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We are given two angles of elevation and the distances from the points of observation to the base of the pyramid. The problem asks to find the height of the pyramid using trigonometric relations.

### Given:
- Angle 1: \( 21^\circ 20' \) (or \( 21^\circ + \frac{20}{60} = 21.33^\circ \))
- Angle 2: \( 13^\circ 20' \) (or \( 13^\circ + \frac{20}{60} = 13.33^\circ \))
- Distance between the two points of observation: \( 134 \text{ feet} \)
- \( x \) = distance from the first point to the base of the pyramid (unknown)
- \( h \) = height of the pyramid (unknown)

We can form two right-angled triangles and use the tangent function for each.

1. **For the closer observation point**:
   \[
   \tan(21.33^\circ) = \frac{h}{x}
   \]
   Therefore, \( h = x \cdot \tan(21.33^\circ) \).

2. **For the farther observation point**:
   \[
   \tan(13.33^\circ) = \frac{h}{x + 134}
   \]
   Therefore, \( h = (x + 134) \cdot \tan(13.33^\circ) \).

Since both expressions equal \( h \), we can set them equal to each other:
\[
x \cdot \tan(21.33^\circ) = (x + 134) \cdot \tan(13.33^\circ)
\]

Now, let's solve this equation to find \( x \), and then use it to calculate \( h \). I'll calculate this now.The height of the pyramid is approximately **81 feet**, rounded to the nearest integer.

Would you like more details or have any questions about the solution? Here are some related questions you could explore:

1. How would the calculation change if the angles of elevation were smaller?
2. What trigonometric functions are most useful for solving similar problems?
3. How could this method be applied to measure the height of a real-world object?
4. What is the importance of converting angles into decimal form?
5. How can we verify the accuracy of the solution through another method?

**Tip**: Always check your angle conversions carefully, especially when dealing with minutes and degrees.

The angle of elevation from a point on the ground to the top of a pyramid is 21°20'. The angle of elevation from a point 134 feet farther back to the top of the pyramid is 13°20'. Find the height of the pyramid.

Learn how to find the height of a pyramid using two angles of elevation, 21°20' and 13°20', with one point 134 feet farther back. This problem uses right triangle trigonometry and the tangent function.

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