In triangle ABC, if angle a = 1 / 4 angle B = 1 / 5 angle c, then what triangle ABC is divided according to the size of angle

solution
A+B+C=180
A=1/4B=1/5C
Qi
B=4A
C=5A
Qi
A+4A+5A=180
∴A=18
∴B=72
C=90
It's a right triangle

Triangle ABC, known AB side length, and B side corresponding angle B, find triangle C side length Note that given the side length a, B and angle B, find the side length C

a/sinA=b/sinB,A=arcsin(asinB/b)
C=180°-A-B
b/sinB=c/sinC
C can be calculated

In the triangle ABC, we know that the three sides a = 7, B = 4 √ 3, C = √ 13. We can find the size of the minimum angle of the triangle ABC and the area of the triangle ABC

Small side to small corner
C = √ 13 min
Cosine theorem:
cosC=(a^2+b^2-c^2)/(2ab)=√3/2
∴C=30°
The area of triangle ABC = 1 / 2 * AB * sinc = 1 / 2 * 7 * 4 √ 3 * 1 / 2 = 7 √ 3

It is known that in the triangle ABC, the complementary angle of angle a is three times that of angle B, and the residual angle of angle B is 30 degrees smaller than that of angle C. the size of three internal angles of triangle ABC is calculated Let me understand the process as much as possible, the best use of equations

DEG
180-A=3B
90-B=C-30
A+B+C=180
This equation should be solved simply

a. B and C are positive integers and satisfy the equation plus ABC + AB + AC + BC + A + B + C + 1 equals 2004, then the minimum value of a + B + C + C is? This is the Ninth "China Cup" test

abc+ab+ac+bc+a+b+c+1=(a+1)(b+1)(c+1)=2004=2*2*3*167
When a + 1 = 2 * 2 = 4, B + 1 = 3, C + 1 = 167, the minimum is
A = 3, B = 2, C = 166 are obtained
a+b+c=171

In △ ABC, given C ^ 2 = a ^ 2 + B ^ 2 + AB, s = 15 √ 3, C = 14, find the length of the other two sides of the triangle

a=10,b=6

. ABC is a three digit number. The sum of the other five three digits is equal to 2743 . abc．

If a + B + C = 13, then ABC = 13 × 222-274

Is there such a three digit ABC, which is equal to the sum of the following three two digits: AB, BC, CA?

From the meaning of the title
a+b+c+10(a+b+c)=100a+10b+c
B + 10C = 89A (a, B, C are natural numbers less than 10)
So there is only one case, a = 1, B = 9, C = 8, which is 198

. ABC is a three digit number. The sum of the other five three digits is equal to 2743 . abc．

The sum of all six three digit numbers composed of a, B and C is equal to (a + B + C) × 222,
Then the sum of the six three digits should be greater than 2743 and less than 3743
A + B + C can only be equal to 13, 14, 15 or 16 because 2743 △ 222 ＞ 123743 △ 222 ＜ 17
If a + B + C = 13, then
.
ABC = 13 × 222-2743 = 143, a + B + C = 1 + 4 + 3 = 8 ≠ 13;
If a + B + C = 14, then
.
ABC = 14 × 222-2743 = 365, a + B + C = 3 + 6 + 5 = 14;
Similarly, when a + B + C = 15 or a + B + C = 16, neither of them is satisfactory
So,
.
abc=365．
A: the three digit number is 365

It is known that a, B and C satisfy ab a+b＝1 3，bc b+c＝1 4，ca c+a＝1 5, then ABC The value of AB + BC + Ca is () A. 1 Six B. 1 Twelve C. 2 Fifteen D. 1 Twenty

From the known, ABC
ac+bc＝1
3，abc
ab+ac＝1
4，abc
bc+ab＝1
5，
Then AC + BC = 3ABC ①, AB + AC = 4abc ②, BC + AB = 5abc ③,
① 2 (AB + BC + Ca) = 12abc,
That is, ABC
ab+bc+ca=2
12＝1
6．
Therefore, a

In triangle ABC, if angle a = 1 / 4 angle B = 1 / 5 angle c, then what triangle ABC is divided according to the size of angle