cho tam giác ABC có góc A,B,C lần lượt TL với 7,5,3 .Hỏi góc ngoài tương ướng TL với số nào?
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AL
3 tháng 2 2021
Gọi 3 góc A,B,C lần lượt là x,y,z
Theo bài ra ta có:
x/7=y/5=z/3 mà x+y+z=180 độ
=> x/7=y/5=z/3=x+y+z/7+5+3=180/15=12
x=12*7=84
y=12*5=60
z=13*3=39
Gọi góc ngoài tại 3 đỉnh A,B,C là a,b,c
Ta có a=y+z=96 , b=x+z=120 , c=y+x=144
=>ƯCLN(a,b,c)=24
=>a=96/24=4
b=120/24=5
c=144/25=6
Vậy các góc ngoài tam giác ABC tỉ lệ với 4,5,6
VN
0
12 tháng 3 2017
Gọi các góc ngoài tưng ứng của tam giác lần lượt là \(m;n;p\)
Tam giác ABC có : \(a+b+c=180^0\) Và \(\frac{a}{7}=\frac{b}{5}=\frac{c}{3}\)
Áp dụng TC DTSBN ta có :
\(\frac{a}{7}=\frac{b}{5}=\frac{c}{3}=\frac{a+b+c}{7+5+3}=\frac{180^0}{15}=12^0\)
\(\Rightarrow a=84^0;b=60^0;c=36^0\)
\(\Rightarrow m=180^0-84^0=96^0\)
\(\Rightarrow n=180^0-60^0=120^0\)
\(\Rightarrow p=180^0-36^0=144^0\)
Ta có ƯCLN(96;120;144) = 24
=> \(m;n;p\) tỉ lệ với (96 : 24); (120 : 24) ; (144 : 24)
=> \(m;n;p\) tỉ lệ với \(4;5;6\)
27 tháng 12 2015
Gọi a,b,c là các góc A,B,C tỉ lệ lần lượt với 7;5;3
a/7=b/5=c/3 va a+b+c=180
Ap dung tinh chat day ti so bang nhau ta co :
a/7=b/5=c/3=a+b+c/7+5+3=180/15=12
Suy ra :a/7=12=>a=12.7=84
b/5=12=>b=12.5=60
c/3=12=>c=12.3=36
****
17 tháng 12 2016
bạn này giải sai rồi ,các góc ngoài tỉ lệ lần lượt với 4;5;6
AT
2
4 tháng 1 2017
Ta có : góc A + góc B + góc C = 180
A : B : C = 3 : 5 : 7
\(\Rightarrow\frac{A}{3}=\frac{B}{5}=\frac{C}{7}\)
Áp dụng tính chất dãy tỉ số bằng nhau ,ta có :
\(\frac{A}{3}=\frac{B}{5}=\frac{C}{7}=\frac{A+B+C}{3+5+7}=\frac{180}{15}=12\)
\(\Rightarrow\hept{\begin{cases}A=12.3=36\\B=5.12=60\\C=7.12=84\end{cases}}\)
15 tháng 6 2022
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