"Related Calculations of Trigonometric Functions" The relationship between the sides and angles of a right triangle PPT courseware 4

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"Related Calculations of Trigonometric Functions" The relationship between the sides and angles of a right triangle PPT courseware 4

Relationship between sides and angles of right triangle

1. The relationship between the three sides of a right triangle: Pythagorean theorem a2+b2=c2.

2. The relationship between the two acute angles of a right triangle: the two acute angles are complementary to each other: ∠A+∠B=90°.

3. The relationship between the sides and angles of a right triangle: acute angle trigonometric functions

sinA=cosB=a/c,

tanA=cotB=a/b,

cotA=tanB=b/a

4. The trigonometric function relationship between two mutually supplementary angles: sinA=cosB, tanA×tanB=1

5. Trigonometric function relationship between the same angles: sin2A+cos2A=1.tanA=sinA/cosA

practice

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°.

Example 1. 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 the distance the cable car rises vertically how many?

As shown in the figure, in Rt△ABC,

∠C=90°,BC=ABsin16°.

Do you know what sin16° is equal to?

You can use a scientific calculator to find: BC=ABsin16° ≈200×0.2756≈55.12.

As shown in the picture, Wuhua Building is 60m away from Xiaowei's home. Xiaowei looked at the building from his window and measured the elevation angle of the top of the building to be 45° and the depression angle of the bottom of the building to be 37°. Find the height of the building (the result is accurate to 0.1m).

As shown in the figure, in Rt△AOC, ∠C=90°,

AC=OCtan45°.

In Rt△OCB, ∠C=90°,

CB=OCtan37°.

AB=AC+BC=60tan50°+60×tan37º≈5.82m

True knowledge is born in practice

As shown in the figure, according to the known data in the figure, find the lengths of the other sides of △ABC, the measures of each angle and the area of ​​△ABC.

As shown in the figure, based on the known data in the figure, find AD.

Teacher expectations:

You can get the success it brings you as a "model".

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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.

"Related Calculations of Trigonometric Functions" The relationship between the sides and angles of a right triangle PPT courseware 3:

"Related Calculations of Trigonometric Functions" PPT courseware on the relationship between the sides and angles of a right triangle 3 Teaching objectives (1) Teaching knowledge points 1. Experience the process of using a calculator to find the corresponding acute angle from the value of a trigonometric function, and further understand the meaning of trigonometric functions. 2. Be able to use a calculator to do related...

"Related Calculations of Trigonometric Functions" Relationship between sides and angles of right triangles PPT courseware 2:

"Related Calculations of Trigonometric Functions" PPT courseware 2 on the relationship between the sides and angles of a right triangle (1) The relationship between the three sides a+b=c (2) The relationship between the two acute angles A+B=90 (3) The relationship between the sides and angles The relationship between sinA=opposite side of A/hypotenuse=a/c sinA=opposite side of B..

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

"Related Calculations of Trigonometric Functions" PPT courseware on the relationship between the sides and angles of a right triangle is as shown in the figure. When the suspension box of the mountain cable car passes through point A and reaches point B, it has traveled 200m. It is known that the angle between the route of the cable car and the horizontal plane is =16 So how far does the cable car go vertically up? On Rt..

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Update Time: 2024-10-05

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

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