**Math Labs with Activity – To Prepare a Clinometer to Measure the Height of an Object**

**OBJECTIVE**

To prepare a clinometer and use it to measure the height of an object (say a lamp post)

**Materials Required**

- A thick chart paper
- A soft-drink straw
- A flexible string
- A small weight (a metal washer)
- A geometry box

**Theory**

Consider an object (e.g., a lamp post) at a distance d from you. Let your height be h_{1} and the height of the lamp post be h_{2}. Let θ be the angle of elevation of the top of the lamp post with respect to your eye. If h = h_{2} – h_{1} then from Figure 42.1 we have h

tan θ = h/d, i.e., h = d tan 0.

height of the lamp post = h_{2} = h + h_{1}= h_{1}+ d tan θ.

**Procedure**

**Step 1:** On the top side of the chart paper construct a large protractor as shown in Figure 42.2.

**Step 2:** Fix the soft-drink straw at the centre point O (as shown in Figure 42.2 using a nail. Ensure that the straw lies at your eye level.

**Step 3:** From the nail suspend a weight using a flexible string as shown in Figure 42.2.

**Step 4:** A clinometer (also called inclinometer, as it is used for measuring the angle of slope, elevation or inclination of an object) is thus prepared.

**Step 5:** Measure the distance d of the object (lamp post) from the clinometer.

**Step 6:** Look through the straw and keep on tilting it till you are able to see the top of the lamp post.

**Step 7:** Hold the clinometer in this position and record the angle of elevation of the top of the lamp post.

**Step 8:** Record your height also.

**Observations and Calculations**

Distance of the object from you = d.

Angle of elevation of the top of the lamp post with respect to your eye = θ.

Your height = h_{1}.

Therefore, height of the lamp post h_{2}=h_{1}+d tan θ.

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