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It is known that the edge length of regular tetrahedron a-bcd is a (four faces are congruent regular triangles), e and F are the midpoint of edges BC and ad respectively. Find the angle formed by EF and ab
Take the midpoint of AC as M. use the assignment method to make the edge length of a-bcd 2. ∵ ACD is an equilateral triangle, AF = DF = 1, ∵ CF ⊥ DF, ∵ CF = √ 3DF = √ 3. ∵ abd is an equilateral triangle, AF = DF = 1, ∵ BF ⊥ DF, ∵ BF = √ 3DF = √ 3. ∵ BF = CF = √ 3, be = CE = 1, ∵ EF ⊥ BC, ∵ EF = √ (BF ^
As shown in the figure, points e, F, G and H are the midpoint of edges AB, BC, CD and Da of parallelogram ABCD respectively Verification: △ bef ≌ △ DGH
It is proved that ∵ quadrilateral ABCD is a parallelogram,
∴∠B=∠D，AB=CD，BC=AD．
And ∵ e, F, G and H are the midpoint of the four sides of the parallelogram ABCD respectively,
∴BE=DG，BF=DH．
∴△BEF≌△DGH．
As shown in the figure, points e, F, G and H are the midpoint of edges AB, BC, CD and Da of parallelogram ABCD respectively Verification: △ bef ≌ △ DGH
It is proved that ∵ quadrilateral ABCD is a parallelogram,
∴∠B=∠D，AB=CD，BC=AD．
And ∵ e, F, G and H are the midpoint of the four sides of the parallelogram ABCD respectively,
∴BE=DG，BF=DH．
∴△BEF≌△DGH．
Given the arc length and radius of the circle, the formula for calculating the center angle of the circle fast
Circumference of circle = 2 π R
An arc is part of a circle, so
Arc length = circumference of the circle * (center angle of the arc / 360 °)
=2 π R * center angle / 360 °
Because 2 π = 360 °
therefore
Sector center angle = arc length / radius
The unit obtained is radians, which should be replaced by angular degrees
The arc length formulas under angle system and radian system are used to calculate the length of the arc corresponding to the center angle of 60 degrees in a circle with a radius of 1m
Angle system: l = (center angle of Arc / 360 °) * circumference
=（60°/360°）*2π
=π/3
Radian system: l = (radian to the center angle of the circle / (2 π)) * circumference
=((π/3)/(2π))*2π=π/3
(Lesson 11 8) calculate the length of the arc corresponding to the center angle of 60 degrees in a circle with a radius of 1m by using the arc length formula under the angle system and the solitude system respectively
Using the arc length formulas under the angle system and the solitude system respectively, calculate the length C of the arc corresponding to the center angle of a = 60 degrees in the circle with radius r = 1m?
C=(2*PI*R)*A/360=(2*PI*1)*60/360=PI/3m
A = 60 degrees = 60 * pi / 180 = pi / 3 radians
C=R*A=1*PI/3=PI/3m
RELATED INFORMATIONS
- 1. The radius of the circle is 240mm. How many degrees is the center angle of the circle opposite to the arc with a length of 500mm on the circle? Why is the answer only positive
- 2. A construction company wants to build an arc-shaped curve with a radius of 30m. The center angle of the arc-shaped curve is 120 °, then the length of the curve is? (π takes 3)
- 3. Given that the chord length of the center angle with radian number 2 is also 2, the arc length of the center angle is () A. 2 B. 2sin1 C. 2sin-11 D. sin2
- 4. Radian system formula about sector arc length and area formula? Derivation formula?
- 5. As shown in the figure, points e, F, G and H are the midpoint of edges AB, BC, CD and Da of parallelogram ABCD respectively Verification: △ bef ≌ △ DGH
- 6. 2. Let a be m × N matrix, B is n × M matrix, and m < n, ab = I is known, where I is an m-order identity matrix. It is proved that the column vector group of B is linear
- 7. Given that a = √ 2, B = 3, the included angle between a and B is 45 °, find the vector a+ λ B and λ When the included angle of a + B is an acute angle, λ Value range of
- 8. If the center angle of an arc is 135 °, and the arc length is equal to 3 times the circumference of a circle with a radius of 5cm, the radius of this arc is______ cm．
- 9. In ⊙ 0, if the length of string AB is equal to the radius, find the degree of the circumferential angle of the arc opposite string ab
- 10. In a circle with radius 1, the length is equal to What is the central angle of the string of 2______ Degrees
- 11. An ant starts from a, crawls along the polygon for a week and returns to point a, then vector AB + vector BC + vector CD + vector de + vector EF + vector FG + vector GA = ()
- 12. Arc length equals________ The central angle of the circle opposite the arc of is called the angle of 1 radian
- 13. There is a curve in the shape of an arc, as shown in the figure. The length of the curve is 12M, and the center angle of the arc is 81 °. Find the radius r of this arc as __ (accurate to 0.1M)
- 14. Using the arc length formulas under angle system and radian system respectively, the length of the arc corresponding to the 60 ° center angle in a circle with a radius of 1m is calculated
- 15. It is known that the arc length of an arc is equal to the side length of the inscribed regular triangle of its circle, then the radian number of the center angle of the arc is __
- 16. How many radians is the center angle of a string with a length equal to 3 times the root of the radius Trouble = give me the process
- 17. On a circle with a radius of 25mm, if the length of an arc is 50mm, the radian number of the center angle of the arc is (). For detailed explanation,
- 18. On a circle with a known radius of 120 mm, the length of an arc is 144 mm. Find the radians of the center angle of the arc Answer: |a| = 144 / 120 = 1.2, so the radian number of the center angle is 1.2 Because there is a formula, l = |a|r: the arc length is equal to the absolute value and half of the center angle (the number of radians) of the arc Product of diameters So in this question, should the answer be that the radian number of the center angle is 1.2 or - 1.2? The question does not say whether the positive angle or the negative angle should be taken into account
- 19. If the arc length of the center angle of 1 radian is equal to 2, the chord length of the center angle is equal to?
- 20. In a circle with a radius of 2, the number of radians of the center angle of the arc with an arc length of 1 is _