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How many degrees is the sum of the internal angles of a triangle
The sum of the interior angles is a fixed value, 180 degrees. You can think of an equilateral triangle. Each angle is 60 degrees,
On Roche geometry and Riemannian geometry
How to explain the two axioms of "from a point outside a line, at least two lines can be made parallel to this line" in Roche geometry and "through a point outside a line, no line can be made parallel to a known line" in Riemannian geometry
Rogowski geometry is actually built on a surface with a negative constant Gaussian curvature. If you learn differential geometry, you can easily understand it
The main reason is that the straight line of this kind of surface is different from the straight line on the plane
Riemannian geometry is on a surface with normal Gaussian curvature, that is, a sphere. It's easy to understand that a line on a sphere is a big circle. You can try it and see if it satisfies the fifth postulate
In the acute triangle ABC, AB is two of the equations X & # 178; - 2 √ 3x + 2 = 0, and the angle AB satisfies 2Sin (a + b) - √ 3 = 0. Find the angle c, edge C and s △ ABC
2sin(A+B)-√3=0
sin(A+B)=√3/2
Sinc = √ 3 / 2, the triangle is an acute triangle, C = 60 degree
From Veda's theorem
a+b=2√3 ab=2
From cosine theorem
c²=a²+b²-2abcosC
=a²+b²-2abcos60°
=a²+b²-2ab(1/2)
=a²+b²-ab
=(a+b)²-3ab
=(2√3)²-3×2
=6
c=√6
S△ABC=(1/2)absinC=(1/2)×2×(√3/2)=√3/2
If the hypotenuse is 2, the area of the triangle will be evaluated as a fixed value no matter what the value of AB is
The perimeter of right triangle is 2 + radical 5, the length of two right sides is ab, and the hypotenuse is 2
So a + B = radical 5
Another right triangle
From Pythagorean Theorem A ^ 2 + B ^ 2 = C ^ 2 = 4
Area of triangle = AB / 2 = ((a + b) ^ 2-A ^ 2 + B ^ 2) / 4 = (5-4) / 4 = 1 / 4
Let a and B be the two right sides of a right triangle. If the perimeter of the triangle is 6 and the length of the hypotenuse is 2.5, then the value of AB is ()
A. 1.5B. 2C. 2.5D. 3
The perimeter of ∵ triangle is 6, the length of hypotenuse is 2.5, ∵ a + B + 2.5 = 6, ∵ a + B = 3.5, ① ∵ A and B are the two right sides of right triangle, ∵ A2 + B2 = 2.52, ② AB = 3 can be obtained from ① and ②, so D
RELATED INFORMATIONS
- 1. In the triangle ABC, BC = B-A and B-A = 80 ° then the cosine of the inner angle c is
- 2. In the triangle ABC, the opposite sides of the three inner angles ABC are ABC, and the angle a is 80 °, a & # 178; = B (B + C), and the degree of angle c is calculated
- 3. In △ ABC, the opposite sides of angles a, B and C are a, B and C respectively. If SINB = 2sinc and A2 − B2 = 32bc, then a=______ ．
- 4. In △ ABC, (a + B + C) (SINB + sinc Sina) = 3bsinc, and Sina = 2sinbcosc, what triangle is △ ABC?
- 5. In the acute triangle ABC, AB > BC > AC, and the maximum internal angle is 24 ° larger than the minimum internal angle, then the value range of ∠ A is______ ．
- 6. In the triangle ABC, the opposite sides of the angle are ABC. If bcosc + ccosb = 2acosa, vector AB * vector AC = 3 and B + C = 5, the value of a is obtained
- 7. If the cosine of their angle is the root of the equation 5x2-7x-6 = 0, then the length of the other side of the triangle is () A. 52B. 213C. 16D. 4
- 8. In the triangle ABC, C = 3 / 4 π, Sina = 5 / 5 root sign, find cosa and SINB, if AB = 2 times root sign 2, find a, B
- 9. A mathematical problem about cosine theorem, will help ah! Thank you~~ Please take a look for me In △ ABC, the opposite sides of angles a, B and C are a, B and C respectively. If (a ^ 2 + C ^ 2-B ^ 2) * tanb = root 3 * AC, then the size of angle B is calculated Solution: CoSb * 2Ac * tanb = radical 3 * AC CoSb * tanb = radical 3 / 2 SINB = root 3 / 2 Why is the answer only 60?
- 10. In △ ABC, a = 12, B = 13, C = 60 ° the solution of this triangle is () A. No solution B. one solution C. two solutions D. indeterminate
- 11. The sum of internal angles of trapezoid and parallelogram is 360 degrees______ (judge right or wrong)
- 12. In △ ABC, if the degree ratio of angle a, angle B and angle c is 2:3:5, then what triangle is △ ABC
- 13. In the triangle ABC, the angle B is equal to 30 degrees, the angle c is equal to 45 degrees, AB is equal to two centimeters, then what is BC equal to
- 14. Known triangle ABC solution triangle. Angle a = 45 degrees, angle B = 75 degrees, B = 8, Angle a equals 60 degrees, angle B equals 45 degrees, a = 3.
- 15. If triangle ABC is equal to triangle def, angle a = 40 degrees, angle e = 70 degrees, BC = a, ab = B, then DF =? The length of DF is
- 16. In a right triangle, the lengths of two right angles are known: 12 meters and 3.6 meters respectively. The length of the hypotenuse and the degree of the minimum acute angle are calculated
- 17. Solving right triangle At the same time, ship a and ship B depart from port a to island B. ship a sails to Island b 60 ° north by west at a speed of 10 knots; ship B sails at a speed of 20 knots, first sailing due east for 1 hour, then arriving at port C to pick up passengers. After staying for half an hour, ship a turns northeast to island B. the speed is still 20 knots There is a lighthouse on Island b, which can be seen within 5 nautical miles of the lighthouse. Ask which ship a or B sees the lighthouse first, and what is the time difference between the two ships? (accurate to minutes, √ 3 = 1.73, √ 2 = 1.41, √ 6 = 2.45)
- 18. A right triangle has an angle of 45 ° and its longest side is known to be 12 cm. The area of this triangle is______ Square centimeter
- 19. The circumference of a right triangle is 36 cm, and the length ratio of the three sides is 3:4:5 (1) How many centimeters are the three sides of this triangle? (2) What's the area of this right triangle in square centimeters?
- 20. The square of the hypotenuse of a right triangle is twice the product of two right angles. This triangle has an acute angle () A. 15°B. 30°C. 45°D. 60°