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P is a point in the regular triangle ABC, PA is equal to 2, Pb is equal to 2 times the root sign 3, PC is equal to 4. Find the length of BC
Rotate the triangle BCP around point C until BC and AC side coincide. Mark the new position of point P as o triangle AOP a p = 2 Ao = 2 root sign 3 and angle PCO = angle BCA = 60 degrees CP = Co, so the triangle CPO is a regular triangle, so Po = 4, so the angle Pao in the triangle apo is Pao = 90 degrees, the angle apo = 60 degrees, the angle AOP = 30 degrees, so the angle AOC = 30 + 60 = 90 degrees
P − ABC, PA = Pb = PC = Then the dihedral angle p-ac-b is 73, ab = 10, BC = 8, CA = 6______ .
Because AB = 10, BC = 8, CA = 6, the bottom is a right triangle
Because PA = Pb = PC=
Therefore, the projection of P on the base is the outer center of the right triangle ABC and the midpoint of ab
Let the midpoint of AB be D, and the vertical AC should be de, and the perpendicular foot should be e. therefore, de should be parallel to BC and de = 1
2BC = 4, so ∠ PED is the plane angle of dihedral angle p-ac-b
Since PD is the central line of the triangle PAB, PD = 4 can be calculated
So tan ∠ ped = PD
DE=
3 so ∠ ped = 60 °
The dihedral angle p-ac-b is 60 degrees
So the answer is: 60 degrees
P is a point in the equilateral triangle ABC, PA = 2, Pb = double root sign 3, PC = 4, find the length of BC I want ideas and processes
So the angle pp'p'p = 60 degrees c'p, P = 60 degrees C, p'p = 60 degrees C, P = 2, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P, P
Let △ ABC be a regular triangle, PA ⊥ plane ABC and PA = Pb = a, find the tangent of a-pc-b
According to the Pythagorean theorem, AC = root 2a, Pb = root 2a, PC = root 3a. At the same time, we can deduce that the triangle PAC congruent triangle CBP, PC is the common side. Through a, we make the vertical PC cross PC at point D and connect BD, then BD is also perpendicular to PC
If PA is perpendicular to the plane ABC, the angle ABC = 90 degrees and PA = AB = BC = a, what is the angle between the straight line Pb and AC?
In the method of taking the midpoint, the midpoint of PA, PC and BC is D, e and BC respectively. De is the median line, de ∥ AC, de = √ 2A / 2. EF ∥ Pb, EF = √ 2A / 2
PA vertical plane ABC, PC = 2A, BC = a, PC and surface ABC form an angle of 30 degrees, angle ABC = 60 degrees, find the tangent of the angle formed by Pb and plane APC Above
From the known AC = √ 3a,
In the triangle ABC, AB ^ 2 + BC ^ 2-2ab * bccos ∠ ABC = AC * 2 is obtained by cosine theorem, and ab = 2A is obtained
If BG is perpendicular to the plane PAC, BG is the distance from point B to plane PAC
In the triangle ABC, from the equal product relation 1 / 2Ab * bccos60 ° = 1 / 2Ac * BG, BG = √ 3A / 3 is obtained
Pb = √ 5a, so PG = √ 42a / 3
If the angle between Pb and APC is θ, then Tan θ = BG / PG = √ 14 / 14
P is a point out of the plane where RT △ ABC is located, ∠ ACB = 90 °, PA = Pb = PC, AC = 18, and the distance from P to plane α is 40? I think it should be the same. Isn't BC in plane α? How is the distance between point and plane defined?
Because PA = Pb = PC, then the projection of point P on the bottom surface ABC is the outer center of triangle ABC
Po ⊥ plane ABC: Po = 40
Take the midpoint D of BC, connect OD, then: OD ⊥ BC, get: PD ⊥ BC, that is, PD is the distance between point P and straight line BC
In the pod of right triangle, Po = 40, OD = (1 / 2) AC = 9, the result is: PD = 41, that is, the distance between point P and BC is 41
The fifth set of RMB front design introduction, please be shorter, about 100 words,
Introduction to the fifth set of RMB 1 banknotes
According to the State Council Order No. 268 of the people's Republic of China on June 30, 1999, the people's Bank of China issued the fifth set of RMB 1 yuan banknotes in the whole country on July 30, 2004. After the new version of RMB was issued, it was equivalent to the current RMB and had the same currency function
1、 Face features
The main color is olive green. The ticket is 130 mm long and 63 mm wide. The main scene on the front is the head of Mao Zedong. On the left is the bank name of the people's Bank of China, Arabic numeral "1", face value of "one circle" and flower patterns. The top left corner is the design of the national emblem of the people's Republic of China. The lower left corner is printed with a two-color horizontal number, and the lower right corner is a Braille face mark. The main scene on the back is the West Lake pattern, At the bottom left is printed "1yuan", and on the upper right is the Chinese phonetic alphabet of "people's Bank of China" and "people's Bank of China" in Mongolian, Tibetan, Uyghur and Zhuang languages
2、 Anti counterfeiting features
（1） Fixed flower watermark: it is located in the left margin of the front, and the orchid watermark with strong stereoscopic sense can be seen from the perspective of light
（2） Hand carved head portrait: the front main scene of Mao Zedong's head, using manual engraving gravure printing technology, vivid, vivid, concave and convex, easy to identify
（3） Invisible denomination number: there is a decorative pattern on the top right of the front. Place the face of the ticket close to the eye, and tilt up and down in front of the light source, and you can see the face number "1"
（4） Offset microfilm: in the offset pattern on the bottom of the back, the words "RMB" and "RMB 1" are printed
（5） Engraving gravure printing: the front main scene of Mao Zedong's head portrait, "people's Bank of China" bank name, face number, Braille face mark, etc. are engraved intaglio printing, with a finger touch has obvious concave and convex feeling
（6） Two color horizontal number: printed on the front, the left part is red, the right part is black
Appreciation of the fifth set of RMB back design Theme: landform Activity suggestion: recognize the famous landforms in the regiment with 5 yuan, 10 yuan, 20 yuan and 50 yuan Activity material (presentation form): describe the landform and genetic characteristics in the pattern of RMB
The fifth set of 5 yuan on the back of Mount Tai and the fifth set of 5 yuan on the back of Mount Tai is Mount Tai. However, this pattern uses the space "montage" technique, which combines the two scenes of "five mountains alone" and the main peak of Mount Tai. In reality, Mount Tai is the highest mountain of Chinese culture, although its altitude is only 1546 meters, The landform of Mount Tai is divided into four types: alluvial proluvial platform, denudation and accumulation hills, tectonic denudation low mountain and erosion structure low mountain. In spatial form, it is from low to high, resulting in the towering trend of mountain peaks and towering in the sky, The formation of a variety of terrain groups combined landscape
At the entrance of Qutang gorge, it is the west gate of the Three Gorges of the Yangtze River, also known as "qutangguan". Under the majestic Baidi City, it is the gateway to Sichuan Basin. From Baidi city to the East, you can enter Qutang gorge, the westernmost of the Three Gorges, with a total length of about 8 km, which is the shortest among the Three Gorges, but is the most majestic and precipitous, The high mountains on both sides of Kuimen are named Baiyan mountain in the South and Chijia mountain in the north. The walls of the two sides of the river stand as if they were made by heaven. The Baiyan mountain is named for the water solution adhered to the rock, mainly containing calcium, and its color is like white salt. Chijia mountain is named because the aqueous solution containing iron oxide adheres to the surface of weathered rock, The earth and stone of this mountain is red, like a person's bare back, so it is called Chijia mountain. Facing each other across the river, one is in red and the other is wrapped in plain. It can be said that the two mountains are limestone. The long-term wind erosion and rain erosion make the rock walls on both sides of the river look like knives and axes cutting, forming a very beautiful fragment landscape, belonging to water erosion landform
Guilin is a world-famous tourist city. The water of Lijiang River is clear and beautiful, and there is no unique karst landform in the world. "Green mountains, beautiful water, strange caves and beautiful rocks" are the "four wonders" of Guilin, However, because the climate is mild and humid, which is conducive to the growth of plants, and Guilin people pay great attention to the greening of stone mountains, many shrubs, trees and vines will grow tenaciously between the rock crevices, which will cover the stone peaks tightly and look green and full of vitality. Guilin is a typical karst landform. The most important feature of karst landform is that under the long-term erosion of running water, On the one hand, it will form various grotesque caves and constantly change its shape; on the other hand, it will grow various kinds of stalagmites, stone curtains and stalactites, which form a wonderful karst cave spectacle
The fifth set of 50 yuan back Potala Palace in Tibet. In order to make the fifth set of 50 yuan coupons, two senior artists from Shanghai banknote printing and mint came to Lhasa for investigation. They searched for a long time, and finally found the "best angle" on the top of a water plant. They took photos and sketched here, and after repeated modification and carving, they found the "best angle", The Potala Palace, built in the 7th century, was built by Songzan Ganbu, the Tibetan king, to marry Princess Wencheng of Tang Dynasty in Tibet. A palace of 999 houses was built on the Hongshan mountain, more than 3700 meters above sea level in Lhasa. The main building of the palace has 13 floors and is 115 meters high
What are the patterns on the back of the fifth set of RMB banknotes in China?
100 yuan: Great Hall of the people
50 yuan: Potala Palace
20 yuan: Guilin landscape
10 yuan: Three Gorges
5 yuan: Mount Tai
1 yuan: the moon in three pools of West Lake
Wujiao: Lotus
A corner: Orchid
RELATED INFORMATIONS
- 1. The fifth set of RMB 2005 edition, 1 yuan, 2 yuan, 5 yuan, 10 yuan, 20 yuan, 50 yuan, 100 yuan, respectively, how many billion yuan were printed? Please be specific
- 2. Xiaodong's mother received 400 yuan of bonus from the unit, including 8 pieces of 2 yuan, 5 yuan and 10 yuan in total, and the number of 5 yuan and 10 yuan is equal. How many pieces of each of these three kinds of RMB? One yuan equation is needed
- 3. Xiao Ming has saved 87.5 yuan, which is 1 yuan and 50 Jiao coins. The number of one yuan coins is three times that of the pentagons. How many are there in each
- 4. A mathematical problem: a total of 30 coins, 1 jiao 5 jiao 1 yuan each 10, take out 15 pieces, exactly 7 yuan
- 5. Can coins be attracted by magnets?
- 6. A commodity is sold at a discount of 15% for the first time and 10% for the second time. The original price of a commodity is 6 yuan cheaper than that of the first time A commodity is sold at a discount of 5% for the first time and 10% for the second time. The second time is 8 yuan cheaper than the first. What is the original price of this product
- 7. The bookstore shipped back a batch of books, 30% on the first day, 160 copies on the second day, and 120 copies left. How many books are there in this batch?
- 8. A, B two people to the bookstore to buy books, a total of 108 yuan, a used his own money 3 4. B used 80% of his own money, and the amount of money left by the two was exactly the same. How much money did they take with them?
- 9. Please recommend some books about animals, such as Shen Shixi's dream of wolf king and insect records. Please send out some special books that can be bought in bookstores,
- 10. What to do with friends and family on weekends Match with Chinese
- 11. When the radius of the circumscribed circle of △ ABC is 1, the opposite sides of angles a, B and C are a, B and C respectively, and the angles a, B and C form an arithmetic sequence. The value range of A2 + C2 is calculated
- 12. In the right triangle ABC, the angle ACB = 90 °, AC = BC, D is the midpoint of BC, CE is perpendicular to ad, BF is parallel to AC Verification of AB vertical bisection DF Point F is on the extension line of CE and BF
- 13. As shown in the figure, the angle B in the right triangle ABC is 90 degrees, the bisector of angle a intersects with point BC at point D, e is a point on AB, de = DC, D is the center of the circle, and D B is the radius of the circle Find that AC is the tangent of circle D
- 14. The circumference of a right triangle is 6 + 2 3. The center line on the hypotenuse is 2. Find the area of the right triangle______ .
- 15. Given that the sum of the two right angles of a right triangle is equal to 8, what is the maximum area of the right triangle?
- 16. If you expand the base of a triangle to eight times its original size, and a half of Gauss's original size, the area of the triangle will be the same A. 6 times B. 1 / 6 C. 4 times D. 1 / 4
- 17. Given that the sum of the two right angles of a right triangle is equal to 8, what is the maximum area of the right triangle?
- 18. As shown in the figure, △ ABC is an isosceles right triangle, ∠ ACB = 90 ° and ad is the center line on the side of BC. Through C, the vertical line of ad is made, which intersects AB at point E and ad at point F. it is proved that ∠ ADC = ∠ BDE
- 19. As shown in the figure, in △ ABC, point D is on BC, ∠ DAC = ∠ ABC, BD = 4, DC = 5, de ‖ AC, where AB is intersected with E, then De is de=___
- 20. As shown in the figure, in △ ABC, ∠ C = 90 °, AC = 12cm, ab = 25cm, point D on BC, de ⊥ AB, perpendicular foot e, and de = DC, then be=______ .