# Finding the Height of a Lamp Pole

- Similar triangles

- Protractor or altimeter
- 100-foot tape measure
- Large mirror
- Graphing calculator

### Topics

Similar triangles, trigonometric functions

### Overview

Have students determine the height of a lamp pole, or some other large object, using trigonometric relationships. Then have students find the height of the object using just linear distance(s) and similar triangles.

### The "Hook"

**Can you find the height of a lamp pole without knowing the angle of elevation and without using a graphing calculator?**

*Critical Question*### The Investigation

Students (in pairs) find the height of a large object on school property, such as a lamp pole or tree, using right angle trigonometry. The teacher then asks the students to describe multiple ways to find the height of the object using just linear distance(s) and similar triangles.

(A) One method could use the length of the shadow of the object compared to the length of the shadow of a student (see Diagram 1). Measure the length of the shadow of the student, the height of the student and the length of the shadow of the object. Have students describe how differences in the heights of the students are accounted for when they find the height of the object.

(B) A second method could use a mirror placed on the ground so that the object could be viewed by a student (see Diagram 2). Then measure the distance from the object to the mirror, mirror to the student, and height of the student. Have different groups explain how they accounted for the differences in the height of the students through the different placements of the mirrors.

### Teaching Tips

- In Method A shadows of the object and the person could align so that the end of the shadow of the person and object are the same point on the ground. Another possibility would be to treat the shadow of the person and the shadow of the object separately.
- Be sure to have the students draw diagrams to show the method they are using. Diagrams will help them see the similar triangles.
- Proportions that give the correct solution are shown here.

### Citation

From the teaching files of Paul R. Lenz.