Science experiments

PHYSICAL SCIENCE LAB
MEASURING THE HEIGHT OF A FLAGPOLE OR BUILDING
USING IT'S SHADOW AND TRIGONOMETRY

INTRODUCTION:

Trigonometry is a powerful tool for science. We can use the basic trigonometric functions to calculate many things. The definition of the three basic trigonometric functions are the most important in trigonometry. Remember, in mathematics, definitions are simply accepted. This means that unlike theorems, we simply accept and use them.

DEFINITION: If is an angle in standard position, and the point (x,y) is any point on the terminal side of other than the origin, then the three basic trigonometric functions of angle are defined as follows:

Function Abbreviation Definition

The sine of = sin =

The cosine of = cos =

The tangent of = tan =

Where x² + y² = r² . That is, r is the distance from the origin to (x,y).

DEFINITION: If is an angle in standard position, and the point (x,y) is any point on the terminal side of other than the origin, then the three basic trigonometric functions of angle are defined as follows:
	Function		Abbreviation	Definition
The sine of	=	sin	=
The cosine of	=	cos	=
The tangent of	=	tan	=
Where x² + y² = r² . That is, r is the distance from the origin to (x,y).

We will make use of the tangent function in this investigation. Values for the tangent of angles can be obtained from trig tables, or from your calculator. We will however, be calculating the tangent from our data and the definition.

MATERIALS:

Stick (a little more than 2.0 meters long)
meter stick
Calculator

PROCEDURE:

1. Measure 2.0 meters from one end of the stick and mark it. The extra is to push into the ground so the stick will stand.

2. Go outside near the building or flagpole you have chosen to measure. With the sun at a good angle, push the extra length of the stick into the ground so that the stick makes a 90 degree angle with the ground, and the 2.0-meter-mark is flush with the ground.

3. Measure the length of the shadow the stick makes, and record in the data table in the unit meters.

4. Measure the length of the shadow made by the building or flagpole, in meters, and record in the data table.

DATA TABLE:

Stick length = 2.0 meters

Length of shadow from stick. _________ meters

Length of shadow from building or flagpole. _________ meters

CALCULATIONS:

5. We need the tangent for angle . We simply plug our data into the formula for tangent. From the drawing above, the stick length is (y), and the shadow length is (x). Keep all the decimal places in your answer. You can round the final answer for the building height.

tan

tan = _______________

There are no units for the tangent of an angle.

6. Now we have all the information needed to find the building height. The triangle made by the building or flagpole and it's shadow is much larger than the one made by the stick. However, the relationships are the same. Therefore, the angle for the building, is the same as for the stick. The shadow of the building is (x) and the height of the building is (y). We simply rearrange the formula to solve for our new (y).

Height of the building = ___________ meters

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