"Starting from the inclination of the ladder" PPT courseware on the relationship between the sides and angles of a right triangle

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"Starting from the inclination of the ladder" PPT courseware on the relationship between the sides and angles of a right triangle

Start with life practice

In a right triangle, if you know one side and an acute angle, can you find the other sides and angles?

Guess how tall this ancient tower is?

Think about it, can you use the mathematics knowledge you have learned to measure the height of this ancient tower?

Mathematics from life

Let’s start with the inclination of the ladder

Ladders are common objects in our daily lives

Can you compare the two ladders which one is steeper? What are your options?

Multiple variations of similar questions

Xiao Ming and Xiao Liang think so, as shown in the picture:

As shown in the picture, Xiao Ming wants to explain the inclination of ladder AB1 by measuring B1C1 and AC1 and calculating their ratio;

Xiaoliang believes that by measuring B2C2 and AC2 and calculating their ratio, it can also explain the inclination of ladder AB1.

Think carefully

The relationship between the sides and angles of a right triangle

(1).What is the relationship between Rt△AB1C1 and Rt△AB2C2?

What if the position of B2 on the ladder is changed (such as B3C3)?

What conclusion do you draw from this?

The definition of tangent is in Rt△ABC. If the acute angle A is determined, then the ratio of the opposite side of the acute angle A to the adjacent side will be determined. This ratio is called the tangent of ∠A, denoted as tanA, that is, tanA=the opposite side of ∠A. /∠A limb

Try it boldly and practice it

1. As shown in the figure, △ABC is an isosceles right triangle. Can you find tanC based on the data given in the figure?

2. As shown in the figure, a person walks 200m from point A at the foot of the mountain to point B at the top of the mountain. It is known that the vertical distance from the top of the mountain B to the foot of the mountain is 55m. Find the slope of the hillside (the result is accurate to 0.001m).

Issues that should be noted in the definition of tangent

1.tanA is defined in a right triangle, and ∠A is an acute angle (pay attention to the combination of numbers and shapes to construct a right triangle).

2.tanA is a complete symbol, representing the tangent of ∠A. It is customary to omit the "∠" sign (note that tanA does not mean tan times A).

3.tanA is a ratio (the ratio of the sides of a right angle, pay attention to the order of the ratios, and tanA�0, unitless).

4.The size of tanA is only related to the size of ∠A, and has nothing to do with the side length of the right triangle.

5. If the angles are equal, the tangent values ​​are equal; the tangent values ​​of two acute angles are equal, then the two acute angles are equal.

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Update Time: 2024-07-29

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