Let the inner angles a, B and C of △ ABC be opposite to a, B and C respectively. We know that a = 4, B = 5 and C = 61. (I) find the size of angle c; (II) find the area of △ ABC

Let the inner angles a, B and C of △ ABC be opposite to a, B and C respectively. We know that a = 4, B = 5 and C = 61. (I) find the size of angle c; (II) find the area of △ ABC

(1) according to the meaning of the topic, a = 4, B = 5, C = 61, from the cosine theorem, we can get COSC = 42 + 52 − (61) 22 × 4 × 5 = − 12, because C is the inner angle of the triangle, that is, C ∈ (0180 °), so C = 120 °; (6 points) (II) from (I), we can get sinc = sin120 ° = 32, and B = 5, a = 4, then

In the triangle ABC, if a = 6, B = 9 ∠ a = 45 ° then the triangle has several solutions

cosA=(b²+c²-a²)/(2bc)=√2/2;
(81+c²-36)/(2×9×c)=√2/2;
c²+45=9√2c;
c²-9√2c+45=0；
Δ=81×2-45×4=162-180＜0；
So there is no solution
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In the triangle ABC, if a: B: C = 9:40:41, then ∠ C = what

Suppose a = 9, then B = 40, C = 41
a^2+b^2=1681=41^2=c^2
So: ABC is RT triangle
So: ∠ C = 90 degree

There are three departments of a.b.c. each of which has 84.56.60 civil servants. If each department has the same proportion of staff reduction, so that only 150 civil servants are left in this organ, how many are left in department C?
The seventh grade of a school organizes students to travel. If some 45 seat buses are rented, 15 people have no seats. If the same number of 60 seat buses are rented, there will be one more, and the rest of the buses are just full. It is known that the daily rent of 45 seat buses is 250 yuan per car, and the daily rent of 60 seat buses is 300 yuan per car. Question: which bus is more cost-effective to rent? How many cars to rent?
It's going to be connected by a linear equation of one variable

First question
Set up C department and leave x people
The meaning is X: 150 = 60: (84 + 56 + 60)
The solution is x = 45
Second question:
The number of buses with 45 seats is X
Then 45x + 15 = 60 (x-1)
How to solve the equation
X=5
It can be seen from the title that a 45 seat bus needs 5 × 250 = 1250
The bus with 60 seats needs 4 × 300 = 1200
So it's more cost-effective to rent a 60 seat bus, four cars

Given a + B + C = 56, a + B + a = 45, a + B-C = 11, find the numbers of a, B and C

a=11.5 b=22 c=22.5

In right triangle ABC, if angle c = RT angle, AC = 8cmbc = 6cm, CD is vertical to AB, then CD =? A.3cm B 4.8cm C 5cm D 10cm

∵∠C＝90
∴S△ABC＝BC×AC/2＝6×8/2＝24
AB＝√（AC²+BC²）＝√（64+36）＝10
∵CD⊥AB
∴S△ABC＝AB×CD/2＝10×CD/2＝5CD
∴5CD＝24
∴CD＝4.8（cm）

In △ ABC, ∠ C = 90 °, 1 = 2, CD = 1.5cm, BD = 2.5cm, find the length of AC

Let de be perpendicular to point E, where de = CD = 1.5, so be = 2 and BDE area of triangle be 1.5. Suppose ACD area of triangle is x, (x + 1.5) / x = 2.5 / 1.5 = 5 / 3, then x = 9 / 4, so 1.5 * AC / 2 = 9 / 4 and AC = 3cm

If AC = 2.4cm, BC = 1.5cm, then the area of △ AEC is______ ．

∵∠ C = 90 °, AC = 2.4cm, BC = 1.5cm, ∵ s △ ABC = 12ac · BC = 12 × 2.4 × 1.5 = 1.8cm2, ∵ CE is the middle line of △ ABC, ∵ AEC area = 12S △ ABC = 12 × 1.8 = 0.9cm2

If AC = 4cm, BC = 3cm, then the area of △ AEC is

Because CE is the middle line of the triangle, point E is the middle point of AB side, so we can make parallel lines he and he of CB through point E
Then he is the median line of the triangle, then he = 1 / 2CB = 3 / 2
So the area of the triangle AEC is equal to ac * he * 1 / 2 = 4 * 3 / 2 * 1 / 2 = 3

If AB = 4cm, BC = 3cm, then the area of △ AEC is____

It's really very simple. First, find out the square of the length of AC = 16-9 = 7, so AC = root 7. The area of triangle ABC is 3 × √ 7 △ 2 = 3 / 2 √ 7. Because e is the middle line of the hypotenuse, the area of triangle AEC is equal to the area of triangle BEC, so the area of triangle AEC = 1 / 2S △ ABC = 3 / 4 √ 7 square centimeter,