"Related Calculations of Trigonometric Functions" PPT courseware on the relationship between the sides and angles of a right triangle

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"Related Calculations of Trigonometric Functions" PPT courseware on the relationship between the sides and angles of a right triangle

As shown in the figure, when the suspension box of the mountain cable car passes from point A to point B, it has traveled 200m. It is known that the angle between the route of the cable car and the horizontal plane is ∠α=16°, then what is the vertical distance of the cable car?

In Rt△ABC, BC=ABsin16°

Do you know what sin16° is?

In Rt△ABC,

BC=ABsin16°≈55.12 (m)

think about it

When the cable car continues from point B to point D, it has traveled another 200m. The angle between the cable car's route from point B to point D and the horizontal plane is ∠β=42°. What else can you calculate from this?

Practice in class

1 Use a calculator to find the values ​​of the following expressions:

(1)sin56°;

(2)sin15°49′

(3)cos20°;

(4)tan29°;

(5)tan44°59′59″;

(6)sin15°+cos61°+tan76°.

2 To climb from the bottom of a mountain to the top of a mountain, a person needs to first climb a 40° hillside for 300m, and then climb a 30° hillside for 100m. Find the height of the mountain (the result is accurate to 0.01m).

Solution: As shown in the figure, according to the meaning of the question, BC=300 m, BA=100 m, ∠C=40°, ∠ABF=30°.

In Rt△CBD, BD=BCsin40°≈300×0.6428=192.8(m)

In Rt△ABF, AF=ABsin30°=100×1/2=50(m).

Therefore, the mountain height AE=AF+BD=192.8+50=242.8(m).

looking for ways

To find the angle with known trigonometric function values, you need to use the second functions of the "sin", "cos", and "tan" keys "sin־¹, cos־¹, tan־¹" and the 2ndf key.

For example: ①It is known that sinA=0.9816, find the acute angle A.

②It is known that cosA=0.8607, find the acute angle A.

③It is known that tanA=0.1890, find the acute angle A.

④It is known that tanA=56.78, find the acute angle A.

Ask students to complete the following exercises independently.

1. Find the size of the acute angle θ according to the following conditions:

(1) tanθ=2.9888; (2) sinθ=0.3957;

(3)cosθ=0.7850; (4)tanθ=0.8972;

(5) sinθ = 1/2; (6) cosθ = √2/2.

Solution: (1) ∠θ＝71°30′2″; (2) ∠θ＝23°18′35″;

(3) ∠ θ＝38°16′46″; (4) ∠ θ＝41°53′54″;

(5) ∠ θ=30°; (6) ∠ θ=45°.

self-assessment

1. It is known that sinθ=0.82904, find the size of the acute angle θ.

Solution: ∠θ≈56°1″

2. A ladder leans against a wall. It is known that the length of the ladder is 4 m, and the end of the ladder on the ground is 2.5 m away from the wall. Find the acute angle between the ladder and the ground.

Solution: As shown in the figure

∵cosα＝2.5/4=0.625

∴∠α≈51°19′4″.

So the ladder and the ground form

The acute angle is about 51°19′4″.

Class summary

1. Master how to use a scientific calculator to find the corresponding acute angle from known trigonometric function values.

2. Further understand the meaning of trigonometric functions.

3. Be able to use scientific calculators to assist in solving practical problems involving calculation of trigonometric function values.

Keywords: teaching courseware on the relationship between the sides and angles of a right triangle, teaching courseware on calculations related to trigonometric functions, 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, Download PPT courseware related to calculation of trigonometric functions, in .ppt format

For more information about the PPT courseware "Related Calculations of Trigonometric Functions of Side-Angle Relationships of Right Triangles", please click on the ppt tag of Related Calculations of Trigonometric Functions of Side-Angle Relationships of Right Triangles.

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Update Time: 2024-07-10

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