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There is a point P in the equilateral triangle ABC. The distances from point P to vertex a, B and C are 3, 4 and 5 respectively. The degree of angle APB is calculated
Rotate △ ABP 60 ° anticlockwise around point a to Δ ACP ', CP' = BP = 4, AP = AP '= 3, ∠ PAP' = 60, ｜ △ app 'is equilateral triangle, ｜ ∠ AP'p = 60 ° and PP' = 3. In △ CPP ', CP' ^ 2 = 25, CP ^ 2 + PP '^ 2 = 25, ｜ ∠ p'pc is right triangle, ∠ pp'c = 90 °, and ∠ APB = ∠ ap'c = 60 ° + 90 °
There is a point P in the equilateral triangle ABC. If the distances from point P to vertex a, B and C are 3, 4 and 5 respectively, what is the angle APB
It's urgent
150 degrees
Read the following materials and solve the problem: (1) as shown in figure (1), there is a point P in equilateral △ ABC. If the distance from point P to vertex a, B and C is 3, 4 and 5 respectively, then ∠ APB=______ Because PA and Pb are not in a triangle, in order to solve this problem, we can rotate △ ABP around vertex a to △ ACP ′______ In this way, we can use the knowledge of congruent triangles to transform the length of three line segments into a triangle, so as to find the degree of ∠ APB. (2) please use the solution method of question (1) to solve the following problem: as shown in figure (2), △ ABC, ∠ cab = 90 °, ab = AC, e and F are the points on BC, and ∠ EAF = 45 ° to prove: ef2 = be2 + FC2
(1) Rotate △ ABP around vertex a to △ ACP ′, ≌ BAP ≌ cap ′, ≌ AB = AC, AP = AP ′, ≌ BAP = ≌ cap ′, ≌ BAC = ≌ Pap ′ = 60 °, ≌ app ′ = 60 ° because B P P 'is not necessarily connected to PC in a straight line, ﹥ p' C = Pb = 4, PP '= PA = 3, PC = 5, ﹥ PP' C = 90 °, ﹥ PP 'C is a right triangle, ﹥ APB = ﹥ AP' C = ﹥ app '+ ﹥ p' PC = 60 ° + 90 ° = 150 °, ﹥ BPA = 150 °; so the answer is: 150 ° and ﹥ ABP; (2) rotate ﹥ ACF clockwise 90 ° around point a to get ﹥ ABG. Connect eg. then ﹥ ACF ≌ ABG. ﹥ Ag = AF, BG = CF In △ AEG and △ AFE, ∵ Ag = AF ∠ gae = ∠ faeae = AE ≌ AEG ≌ △ AFE. ≌ EF = eg, and ∵ GBE = 90 °, be2 + BG2 = EG2, that is, be2 + CF2 = ef2
Special relativity effect slows down motion clock
Confirmed video
If you make a video, it will be an extremely long video, and it will be divided into two screens equally. If you delete the long process in the middle, it will affect the credibility of the video
Calculation: 1 / x + 1 / 2x + 1 / 3x (with process)
Hello
1/x+1/2x+1/3x
=6/6x+3/6x+2/6x
=11/6x
If you don't understand, you can ask. If it helps, remember to adopt it,
Thank you and wish you progress in your study!
As shown in the figure, four identical small rectangles and one small square are inlaid into a square pattern. The known area of the pattern is 49, and the area of the small square is 4. If x and y are used to represent the length of the two sides of the small rectangle (x > y), please observe the pattern and write three equations represented by X and y
∵ the area of the pattern is 49, the area of the small square is 4, the side length of the pattern is 7, the side length of the small square is 2, the countable equation can be as follows: x + y = 7, x = y + 2, (x + y) 2 = 49, (x + y) 2 = (2Y + 2) 2, (x + y) 2 = 4xy + 4 (choose any three)
It is known that the rated frequency of three-phase asynchronous motor is 50 Hz and the rated speed is 570 R / min. what is the number of poles and the rated slip of the motor?
1. According to the formula of asynchronous motor, n = 120F / P, P is the number of motor poles, 50 Hz, 570 rpm
The number of poles is integer, so p = 10 poles
2. When p = 10 is brought in, the synchronous speed = 120 * 50 / 10 = 600rpm can be obtained
3. Transfer rate = (600-570) / 600 = 0.05 = 5%
Mathematical equation of grade two
180÷x＋180÷y＝360
How to solve 120 △ x + 240 △ y = 360?
Divide the left side of the equation
180x+180y
————=360①
xy
240x+120y
————=360②
xy
180x+180y=240x+120y=360xy
60x=60y
x=y
Substituting x = y into (1) yields
180x+180x
————=360
x^2
360/x=360
x=1
y=x
So y = 1
A rectangle is 18cm in length and 24cm in width. This rectangle can be covered with square paper with several centimeters in side length
A 6cm square, a total of 12, can be well paved
How to calculate the surface area and volume of cube and cuboid
Surface area of cube = 6 * side length * side length
Square volume = side length * side length * side length
Surface area of cuboid = (L * W + L * H + W * h) * 2
RELATED INFORMATIONS
- 1. There is a point P in the equilateral triangle ABC. If the distances from point P to points a, B and C are 3, 4 and 5 respectively, what is the degree of ∠ APB
- 2. If AB = BC, then point B is the midpoint of AB, which is a false proposition
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