"Solving Right Triangles" Acute Trigonometric Functions PPT Courseware 5

Description

"Solving Right Triangles" Acute Trigonometric Functions PPT Courseware 5

learning target

1. Understand the concepts of elevation and depression angles, and be able to apply knowledge of acute angle trigonometric functions to solve relevant practical problems;

2. Cultivate students’ ability to analyze and solve problems.

(1) The relationship between the three sides a2+b2=c2

(2) The relationship between two acute angles ∠A＋∠B＝90°

(3) Relationship between corners

sinA=Opposite side/hypotenuse of ∠A=a/c sinA=Opposite side/hypotenuse of ∠B=b/c

cosA=∠A’s adjacent/hypotenuse=b/c cosA=∠B’s adjacent/hypotenuse=a/c

tanA=Opposite side/adjacent side of ∠A=a/b tanA=Opposite side/adjacent side of ∠B=b/a

[Example 1] On October 15, 2003, the "Shenzhou" 5 manned spacecraft was successfully launched. After the spacecraft completes its orbit change, it will operate in a circular orbit 350km above the earth's surface. As shown in the figure, when the spacecraft moves directly above point P on the earth's surface, what is the farthest point on the earth that can be directly seen from the spacecraft? What is the distance between this farthest point and point P? (The radius of the earth is about 6 400km, take 3.142, and keep the result as an integer)

[Analysis] The farthest point on the earth that can be directly seen from the spacecraft should be the tangent point when the line of sight is tangent to the earth.

definition

When measuring, when looking from bottom to top, the angle between the line of sight and the horizontal line is called the elevation angle; when looking from top to bottom, the angle between the line of sight and the horizontal line is called the angle of depression.

[Example 2] The detector of the hot air balloon shows that the elevation angle of the top of a tall building when viewed from the hot air balloon is 30°, and the depression angle of the bottom of the tall building is 60°. The horizontal distance between the hot air balloon and the tall building is 120m. This tall building has How high (result to one decimal place).

[Analysis] We know that among the angles between the line of sight and the horizontal line, the line of sight above the horizontal line is the elevation angle, and the line of sight below the horizontal line is the depression angle. Therefore, in the figure, � =30°, β=60°.

Practice in class

1. (Qinghai High School Entrance Examination) As shown in the figure, the depression angles of the bottoms of buildings A and B measured from hot air balloon C are 30° and 60° respectively. If the height CD of the balloon at this time is 150 meters, and points A, D, and B On the same straight line, the distance between buildings A and B is ( )

A.150√3 meters B.180√3 meters

C.200√3 meters D.220√3 meters

2. (Zhuzhou High School Entrance Examination) As shown in the picture, Kong Ming is carrying a bucket of water, starting from the foot of the mountain and walking up the hillside that is angled with the ground, delivering water to Grandma Wang’s house on the mountain (location B) who is short of water due to drought this spring. , AB=80 meters, then the height that Kongming ascends from A to B is _____ meters.

[Analysis] According to the question, ∠ACB=90°. So sin∠BAC=sin30°=BC/AB=BC/80=1/2

So BC=40 (meters).

【Answer】40

3. There is a flagpole AB on building BC. The elevation angle of top A of the flagpole is 60° when viewed from D 40m away from BC. The elevation angle of bottom B is 45°. Find the height of the flagpole (accurate to 0.1m)

[Analysis] In the isosceles triangle BCD, ∠ACD=90°, BC=DC=40m,

In Rt△ACD: tan∠ADC=AC/DC

∴AC=tan∠ADC×DC

=tan54°×40≈55.1m

So AB=AC-BC=55.1-40=15.1m

Answer: The height of the chess pole is 15.1m.

Summary of this lesson

The general process of using the knowledge of solving right triangles to solve practical problems is:

1. Abstract practical problems into mathematical problems;

(Draw a plane figure and convert it into a problem of solving a right triangle)

2. According to the characteristics of the conditions, appropriately select acute angle trigonometric functions to solve the right triangle;

3. Get answers to math problems;

4. Get answers to practical questions.

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For more information about the PPT courseware "Solving Trigonometric Functions of Acute Angles in Right Triangles", please click the "Solving Trigonometric Functions of Acute Angles in Right Triangles ppt" tab.

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"Solving Right Triangles" PPT Courseware 2:

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"Applications of Solving Right Triangles" PPT courseware:

"Solution to Right Triangle" PPT courseware 2 Review the past and learn new things 1. The relationship between the sides and angles of a right triangle: (1) The relationship between angles: A+B = 90; (2) The relationship between sides: a2+b2=c2; (3) Angle and side The relationship between: sinA=a/c, cosA=b/c, tanA..

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Update Time: 2024-10-05

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