"Measuring the height of an object" PPT courseware on the relationship between the sides and angles of a right triangle

Description

"Measuring the height of an object" PPT courseware on the relationship between the sides and angles of a right triangle

learning target:

1. Be able to make relevant reasoning and further understand the meaning of trigonometric functions.

2. Be able to calculate trigonometric function values ​​for angles of 30°, 45°, and 60°.

3. Be able to explain the size of the corresponding acute angle based on the trigonometric function values ​​of 30°, 45°, and 60°.

Self-study and clearing up doubts

Activity topic: Use the relationship between the sides and angles of a right triangle to measure the height of an object.

Activity method: group activities or whole-class exchange and discussion.

Activity tools: Inclinometer (or theodolite, goniometer, etc.), tape measure, etc.

Activity 1: Measuring the tilt angle (elevation or depression angle)

To measure the inclination angle, you can use an inclinometer. A simple inclinometer consists of a dial, a plumb and a support rod (as shown in the picture).

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

Insert the support pole vertically into the ground so that the center line of the support pole and the plumb line coincide with the 00 mark of the dial. At this time, the top line PQ of the dial is in the horizontal position.

Rotate the dial so that the diameter of the dial is aligned with the target M, and note the degree pointed by the plumb line at this time.

Activity 2: Measure the height of the object that can be reached from the bottom.

The so-called "bottom can be reached" means that the distance between the measuring point and the bottom of the measured object can be directly measured without any obstacles on the ground.

Proceed as follows:

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

think:

How to measure the height of an object whose bottom is inaccessible.

The so-called "bottom is not accessible" means that the distance between the measuring point and the bottom of the measured object cannot be measured directly on the ground.

To measure the height of an object MN, is it enough to use a tilter to measure the elevation angle once?

As shown in the figure, to measure the height of object MN, you can follow the following steps:

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

2. Place an inclination measurement at B between the measuring point A and the object (A, B and N are on a straight line), and measure the elevation angle of M ∠MDE=β.

3. Measure the height of the inclinometer AC=BD=a, and the distance between measuring points A and B AB=b.

On-site training

1. As shown in Figure 1-16, on the top C of the 20-meter-high building CD, the elevation angle of tower top A is measured to be 60°, and the depression angle of tower bottom B is measured to be 30°, then the tower height AB = ___ meters;

2. As shown in Figure 1-17, Xiao Ming wanted to measure the height of telephone pole AB, and found that the shadow of the telephone pole fell exactly on the ground BC and the slope CD. It was measured that BC = 10 meters, CD = 4 meters, and CD is equal to the ground forms an angle of 30°, and the shadow length of the 1-meter pole is measured to be 2 meters, then the height of the telephone pole is ____ meters.

Keywords: teaching courseware on the relationship between the sides and angles of a right triangle, teaching courseware on measuring the height of an object, Beijing Normal University edition mathematics PPT courseware for the second volume of the ninth grade, downloading the ninth grade mathematics slide courseware, downloading PPT courseware on the relationship between the sides and angles of a right triangle, measurement Height of objects PPT courseware download, .ppt format

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

"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 inclination angle You can use an inclinometer to measure the inclination angle. ----A simple inclinometer consists of a dial, a plumb bob and a support rod. The steps for using an inclinometer to measure the inclination angle are as follows: 1. Hold the support...

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Update Time: 2024-11-22

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

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