"Solving Right Triangles" Acute Trigonometric Functions PPT Courseware 3

Description

"Solving Right Triangles" Acute Trigonometric Functions PPT Courseware 3

problem situation

In order for people to safely climb to the top of a ladder leaning against the wall, the angle α between the ladder and the ground must generally satisfy 50° ≤ α ≤ 75°. There is a 6m long ladder. Question:

(1) How high is the highest bungalow that can be safely climbed using this ladder? (Accurate to 0.1m)

The larger the angle α, the higher the climb.

This problem boils down to: In Rt△ABC, it is known that ∠A= 75° and the hypotenuse AB=6, find the length of BC

(2) When the bottom of the ladder is 2.4m away from the wall, what is the angle α between the ladder and the ground (accurate to 1°)? Can people use this ladder safely at this time?

This problem boils down to: In Rt△ABC, it is known that AC=2.4m and the hypotenuse AB=6, find the measure of the acute angle α?

(3) How far can the bottom of the ladder be from the wall? (accurate to 0.1m)

The smaller the angle α, the farther the bottom of the ladder is from the wall.

This problem boils down to: In Rt△ABC, it is known that ∠A= 50° and the hypotenuse AB=6, find the length of AC

Explore: In Rt△ABC,

(1) According to ∠A= 75° and hypotenuse AB=6, can you find the other elements of this triangle?

(2) According to AC=2.4m and hypotenuse AB=6, can you find the other elements of this triangle?

(3) According to ∠A=60°, ∠B=30°, can you find the other elements of this triangle?

Among the six elements of a right triangle, except for the right angle, if you know two elements (at least one of which is a side), you can find the remaining three elements.

Consolidation exercises

1. In Rt△ABC, ∠C=90°, solve the right triangle according to the following conditions

(1)a=30,b=20

(2)∠B=72°, c=14

Try it: Do you have any other methods? Ask students to try these two methods. (Group work)

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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.

"Application of Solving Right Triangles" PPT Courseware 2:

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"Solving Right Triangles" PPT Courseware 2:

"Solving Right Triangles" PPT Courseware 2 There are four basic types of right-angled triangles: (1) The hypotenuse and the right-angled side are known; (2) The hypotenuse and an acute angle are known; (3) The hypotenuse and an acute angle are known; ( 4) Given a right angled side and an acute angle, the solution steps are as follows: 1. (3 points)..

"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: 2024-09-12

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