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Authoritative PPT Summary
"Solving Right Triangles" Acute Trigonometric Functions PPT Courseware 2
learning target
1. Understand the concept of right triangle;
2. Explore the minimum number of elements required to solve a right triangle;
3. Be able to use formulas to solve right triangles.
Solving Right Triangles
1. The relationship between the three parties:
a2+b2=c2
2.The relationship between two acute angles:
∠A+∠B=90°
3. The relationship between corners
Sine function: sinA=opposite/hypotenuse of ∠A
Cosine function: cosA=liminal/hypotenuse of ∠A
Tangent function: tanA=opposite/adjacent side of ∠A
Knowledge explanation
If you know two elements of the five elements (with at least one edge), you can find the remaining three elements.
In a right triangle, except for right angles, the process of finding unknown elements from known elements is called solving a right triangle.
As shown in the figure, in Rt△ABC, ∠C=90°, ∠B=42°6′, c=287.4. Solve this right triangle.
Analysis: ∠A=90°-42°6′=47°54′
From cosB=a/c, we get a=c·cosB=287.4×0.7420=213.3
From sinB=b/c, we get b=c·sinB=287.4×0.6704=192.7
Track training
1. (2010·Jiangxi High School Entrance Examination) As shown in the figure, the top angle of the tree measured from point C is 33º, BC=20 meters, then the height of the tree AB=_____ meters (calculate with a calculator, the result is accurate to 0.1 meters)
Analysis: From tanC=AB/BC, we get
AB=BC·tanC=20×tan33°=13.0
Answer: 13.0
summary:
To solve a right triangle, there are only two situations:
(1) Two sides are known;
(2) One side and one acute angle are known
Practice in class
1. Solve the right triangle according to the following conditions. (accurate to 0.01)
(1) In Rt△ABC, ∠C=90°, �=30, ∠B=80°;
(2) In Rt△ABC, ∠C=90°, c=8, b=4.
2. In ABCD, AB∥CD, AB=4, CD=8, AD=6, ∠D=43°, find the area of the trapezoid. (accurate to 0.01)
Summary of this lesson
Through this lesson, we should master:
1. Understand the concept of right triangle;
2. Explore the minimum number of elements required to solve a right triangle;
3. Be able to use formulas to solve right-angled triangles. Be able to transform mathematical problems into solving right-angled triangle problems.
4. Don’t forget the mathematical thinking method of “turning a slope into a straight line”!
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