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In △ ABC, 2b = a + C, B & # 178; = AC, then △ ABC must be () A. Acute triangle B, obtuse triangle C, isosceles triangle D, equilateral triangle The scope is the five required exercises of sine theorem and cosine theorem in mathematics,
Because in △ ABC, a + B + C = 180 degrees
When 2B = a + C, 3b = 180 degree
So B = 60 degrees
And B & # 178; = = A & # 178; + C & # 178; - 2accosb, and B & # 178; = AC,
So AC = A & # 178; + C & # 178; - AC
That is, a & # 178; + C & # 178; - 2Ac = 0
That is (A-C) ² = 0
That is, a = C
And because B = 60 degrees
So △ ABC must be (D, equilateral triangle)
As shown in the figure, in the triangle ABC, it is known that the angle B is equal to 60 degrees, D is a point on BC, and ad = AC
Make a little E on the BC extension line to make CE = BD, connect AE, because ad = AC, so the triangle ADC is isosceles triangle, ∠ ADC = ∠ ACD, so ∠ ADB = ∠ ace, and ∵ d = AC, Ba = Ce (edge), so △ abd is all equal to △ ace, so AB = AE, △ Abe is isosceles triangle, and because ∠ B is equal to 60 °, so △ AB
In the acute angle △ ABC, it is known that the edges of the inner angles a, B and C are a, B and C respectively, and satisfy 2sinb (2cos2b2-1) = - 3cos2b. (1) find the size of B; (2) if B = 2, find the maximum area of △ ABC
(1) From 2sinb (2cos2b2-1) = - 3cos2b, 2sinbcosb = sin2b = - 3cos2b, ∩ tan2b = - 3 (4 points) ∵ B is an acute angle, that is, 0 ∵ 2B ∵ π, ∵ 2B = 2 π 3, ∵ B = π 3 (6 points) (2) ∵ B = π 3, B = 2, ∵ from the cosine theorem B2 = A2 + c2-2accosb: 4 = A2 + C2 AC ≥ 2
A passenger car and a freight car run in the same direction on parallel tracks. The length of the passenger car is 200 meters, and the length of the freight car is 310 meters. The speed ratio of the passenger car and the freight car is 4:3. If the passenger car chases the freight car from the rear, the time from the front to the rear is more than 2 minutes. The speed of the two trains can be calculated
2 minutes = 120 seconds, so the speed difference between the two cars is (200 + 310) △ 120 = 4.25 M / s. suppose that the speed of passenger cars is 4x M / s and that of freight cars is 3x M / s. according to the meaning of the question, we can get the equation: 4x-3x = 4.25, & nbsp; & nbsp; & nbsp; X = 4.25, then the speed of passenger car is: 4 × 4.25 = 17 m / s, the speed of freight car is: 3 × 4.25 = 12.75 M / s, a: the speed of passenger car is 17 m / s, the speed of freight car is 12.75 M / s
For two trains, the length of passenger cars is 200 meters, 300 meters per second; for freight cars is 300 meters, 20 meters per line. After two trains go up on the parallel track for a few seconds, the passenger cars overtake the freight cars. If the two trains run in opposite directions, how many seconds does it take from meeting to passing by the wrong train?
The bus is 200 meters long, 300 meters per second; the freight car is 300 meters long, 20 meters per second. The two cars go hand in hand, and after a few seconds on the parallel track, the bus will overtake the freight car. If the two cars are facing each other, how many seconds will it take from meeting to passing by?
Answer 1: 200 / (300-20) = 5 / 7 seconds
2: (300 + 200) / (300 + 20) = 25 / 16 seconds
The two trains are 200 meters long, 50 meters per second, and the freight train is 300 meters long, 40 meters per second. The two trains go together on the track. After a few seconds, the passenger train overtakes the freight train
200÷(50-40)=20s
A bus is 200 meters long and a train is 184 meters long, running on parallel tracks. If the train is in front, the time required for the bus to overtake the truck from behind is 24 hours
Second, if you travel in opposite directions, the time of meeting is 6 seconds, find the speed of the two cars
Let the speed of passenger cars be x m / s and that of freight cars be y m / s
(200+184)/(x-y)=24
(200+184)/(x+y)=6
x=40
y=24
The speed of passenger cars is 40 m / s and that of freight cars is 24 m / s
The bus is 200 meters long, 30 meters per second, and the truck is 300 meters long, 20 meters per second. The two cars are moving in the same direction on the parallel track. How many seconds later does the bus surpass the truck
Because the bus is at the same speed, the distance it exceeds is 200 meters, and the difference between their speeds is 10 meters per second
Facing each other, the total distance is 200 + 300 = 500 meters, the speed is 30 + 20 = 50 meters per second, so it takes 10 seconds
It is known that a = B × 1 / 3 = C × 1 and 1 / 5 = D × 11 / 12 (a, B, C, D are not equal to 0). Please arrange a, B, C, D in the order from big to small
1/3c
A is equal to 3 / 7, B is equal to 11 / 12, C is equal to 15 / 15 (and they are not equal to 0). Please arrange a, B, C from small to large and explain the reason
a b c
Because a = 3 / 7
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