"Starting from the inclination of the ladder" The relationship between the sides and angles of a right triangle PPT courseware 4

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"Starting from the inclination of the ladder" The relationship between the sides and angles of a right triangle PPT courseware 4

A right-angled triangle is formed between the ladder, the ground and the wall. The vertical height of the ladder and the horizontal distance of the ladder can be regarded as its right-angled sides, and the ladder can be regarded as the hypotenuse.

Example 1: As shown in the figure, which ladder is steeper, AB or EF? How do you judge?

You can also judge by the height of the top of the ladder on the wall and the distance of the bottom of the ladder from the wall.

Example 2: As shown in the figure, which ladder is steeper, AB or EF? How do you judge?

A ladder is equally steep if the ratio of its vertical height to its horizontal distance is the same.

What if you change B2's position on the ladder arbitrarily? What do you think?

The size of ∠A is determined, and the ratio of the opposite side to the adjacent side of ∠A remains unchanged.

If the size of ∠A is changed, will the ratio of the opposite side to the adjacent side of ∠A change accordingly?

As the size of ∠A changes, the ratio of the opposite side to the adjacent side of ∠A changes accordingly.

What conclusion do you draw from this?

When the acute angle of a right triangle is determined, the ratio of its opposite side to the adjacent side is also uniquely determined; the ratio has nothing to do with the size of the triangle, but is only related to the size of the inclination angle.

The slope of a slope is often expressed by the slope. For example, if a hillside rises by 60m for every 100m of advancement in the horizontal direction, the slope of the hillside

i=tanα=60/100=3/5

1. The angle (α) between the slope surface and the horizontal surface is called the slope angle

2. The ratio of the vertical height and horizontal width of the slope is called slope i (or slope ratio), that is, the slope is equal to the tangent of the slope angle.

3. The greater the slope, the steeper the slope.

Challenge yourself

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).

Keywords: Teaching courseware on the relationship between the sides and angles of a right triangle, teaching courseware starting from the inclination of the ladder, Beijing Normal University edition mathematics PPT courseware for the second volume of the ninth grade, downloading the ninth grade mathematics slide courseware, PPT courseware on the relationship between the sides and angles of a right triangle Download, start with the inclination of the ladder PPT courseware download, .ppt format

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Update Time: 2024-10-04

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