"Measuring the Height of an Object" The relationship between the sides and angles of a right triangle PPT courseware 2

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"Measuring the Height of an Object" The relationship between the sides and angles of a right triangle PPT courseware 2

1. How to measure the tilt angle

An inclinometer can be used to measure the tilt angle. ----A simple tilter consists of a dial, a plumb bob and a support rod

The steps for measuring tilt angle using an inclinometer are as follows:

1. Insert the bracket vertically into the ground so that the center line and plumb line of the bracket coincide with the 0° scale line of the dial. At this time, the top line PQ of the dial is in a horizontal position.

2. Turn the turntable so that the diameter of the dial is aligned with the target M, and record the degree pointed by the plumb line at this time.

Measure the height of an object with direct reach from the bottom:

1. Install an inclinometer at measuring point A and measure the elevation angle of M ∠MCE=α;

2. Measure the horizontal distance AN=l from the measuring point A to the bottom N of the object;

3. Measure the height of the inclinometer AC=a, and you can find the height of MN.

MN=ME+EN=l·tanα+a

Life application

As shown in the picture, a middle school hangs some colorful flags between the top of the main building and the top of the gate. After measurement, the height of the gate is 5m. The distance between the gate and the main building is 30m. The elevation angle of the top of the main building measured at the gate is 30°. At that time, the tilter was 1.4m from the ground. Find the height of the main building of the school (accurate to 0.01 m)

Solution: As shown in the figure, draw EM perpendicular to CD at point M. According to the meaning of the question, we can know

EB=1.4m, ∠DEM=30°, BC=EM=30 m, CM=BE=1.4m

In Rt△DEM, DM=EMtan30°≈30×0.577 =17.32(m)

CD=DM+CM=17.32+1.4=18.72(m)

To measure the height of an object whose bottom is not directly accessible:

1. Install an inclinometer at measuring point A and measure the elevation angle of M at this time ∠MCE=α;

2. Install an inclinometer at B between the measuring point A and the object, and measure the elevation angle of M at this time ∠MDE=β;

3. Measure the height of the inclinometer AC=BD=a, and the distance between measuring points A and B AB=b. Based on the measurement data, the height of the object MN can be found.

In-class development applications

1. (2005 Shenzhen) The height of building AD is 100 meters. There is tower BC in the distance. Someone measured the elevation angle of tower top B at point A at the bottom of the building to be 60°. He climbed to the top of the building D and measured point B at the top of the tower. If the angle of elevation is 30°, find the height of the tower BC.

2. As shown in the figure, at A, 150 meters away from the iron tower, the elevation angle of the top of the tower is 30° measured with a goniometer. It is known that the height of the goniometer AD=1.5 meters, find the height BE of the iron tower.

Operation

1. Make a simple inclinometer in groups.

2. Select an object whose bottom can be reached, measure its height and write an activity report, explaining the activity topic, measurement diagram, measured data and calculation process, etc.

3. Select an object whose bottom is inaccessible, measure its height and write an activity report, explaining the activity topic, measurement diagram, measured data and calculation process, etc.

(The table below is for reference)

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"Measuring the Height of an Object" PPT courseware on the relationship between the sides and angles of a right triangle:

"Measuring the Height of an Object" PPT courseware on the relationship between the sides and angles of a right triangle. Learning objectives: 1. Be able to make relevant reasoning and further understand the meaning of trigonometric functions. 2. Be able to calculate the trigonometric function values ​​of 30, 45 and 60 angles. 3. Able to use triangles of 30, 45 and 60...

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Update Time: 2024-07-29

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade Mathematics Volume 2 industry PPT template

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