Using the Quadrant. Protractor. Eye Piece. You can measure angles of incline from 0º ( horizontal ) to 90º (vertical ). Ignore measurements >90º.

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1 Using the Quadrant Eye Piece Protractor Handle You can measure angles of incline from 0º ( horizontal ) to 90º (vertical ). Ignore measurements 90º. Plumb Bob ø <----Read angle of incline (ø) here. Eye ø

2 Using the Quadrant To Make a Similar Triangle. Use the quadrant to measure the height of tall objects in an indirect manner. First, locate yourself on a piece of ground that is level with the object to be measured. The object's base and your feet should be on the same horizontal plane. Measure the distance from your feet to the base of the object and record it on the diagram. Choose a multiple of ten feet (or other linear unit ) for this distance to simplify calculation. Second, walk to the object and mark it with a piece of marking tape at your eye level.. The quadrant should read 0º when you aim it at the eye level tape mark. Measure this height and record it on the diagram. Object to be measured Next, aim the quadrant at the top of the object to be measured. Aim the quadrant at the top of the object. - Have your partner read the quadrant's protractor as you hold it steady. The angle of incline should be between 0º and 90º. After that, record your angle of incline on the diagram. Finally, use these measurements to determine the object's height using the graph paper worksheet. Angle of incline: What is your eye level height? Sight a level line and mark the object at that height. Marking tape Make sure that you add your eye height to your height calculation. What is the distance to the object? Measure this distance accurately with a tape measure. < Level ground- - -

3 Using the Quadrant To Determine the Opposite Side Using Tangent. Use the quadrant to measure the height of tall objects in an indirect manner. First, locate yourself on a piece of ground that is level with the object to be measured. The object's base and your feet should be on the same horizontal plane. Measure the distance from your feet to the base of the object and record it on the diagram. Choose a multiple of ten feet (or other linear unit ) for this distance to simplify calculation. Second, walk to the object and mark it with a piece of marking tape at your eye level. Measure this height and record it on the diagram. Third, aim the quadrant at the object to be measured. The quadrant should read 0º when you aim it at the eye level tape mark. - Have your partner read the quadrant's protractor as you hold it steady. Aim the quadrant at the top of the object. Have your partner read the quadrant as you hold it steady. The angle of incline should be between 0º and 90º. Record your angle of incline on the diagram. Object to be measured Finally, Substitute measured values for variables on the following tangent worksheet.. Angle of incline: What is your eye level height? Sight a level line and mark the object at that height. Marking tape Make sure that you add your eye height to your height calculation. Measure this distance accurately with a tape measure. < Level ground- - -

4 Using the Quadrant To Find The Height of an Object Using the Tangent Function. Side opposite Ø Object ( Ø Use the Quadrant to find this angle(ø ). Measured side adjacent to Ø = What is Ø? What is Tan Ø? (Find this on your calculator, or from a Tangent table.) How long is the side adjacent Ø? The side opposite to Ø = "H" Tan Ø = So... Tan Ø ( Side Adjacent ) = Side Opposite Substitute measured values, then evaluate: ( ) = H

5 Make a similar triangle to measure indirectly. Using the Quadrant Mark the angle of incline on the protractor. Vertical scale = horizontal scale. 90º 80º 70º 60º 50º 40º 30º 20º 10º v For estimation purposes only.

6 Make a similar triangle to measure indirectly. Using the Quadrant Mark the angle of incline on the protractor. Mark the distance to the object on the horizontal scale. Draw a vertical line at that point. Connect the protractor's vertex mark "V" with the angle you marked, then extend this line to the vertical line you drew. This intersection marks the object's height from your eye level. Read this vertical distance from the scale on the right. 60 feet 50 feet 40 feet 30 feet 90º 80º 70º 60º 50º 40º 20 feet 30º 20º 10º 10 feet v For estimation purposes only. 30 feet 40 feet 50 feet 60 feet 70 feet 80 feet 90 feet 100 feet

7 Make a similar triangle to measure indirectly. Using the Quadrant Mark the angle of incline on the protractor. Mark the distance to the object on the horizontal scale. Draw a vertical line at that point. Connect the protractor's vertex mark "V" with the angle you marked, then extend this line to the vertical line you drew. This intersection marks the object's height from your eye level. Read this vertical distance from the scale on the right. 120 feet 100 feet 80 feet 60 feet 90º 80º 70º 60º 50º 40º 40 feet 30º 20º 10º 20 feet v For estimation purposes only. 60 feet 80 feet 100 feet 120 feet 140 feet 160 feet 180 feet 200 feet