An orthocenter is the intersection of three <u>Altitudes in a triangle</u>
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Explanation:
Cos milky said it.
Solution :
Given


Let the initial approximation is 
So by Newton's method, we get






are identical up to eight decimal places.
The approximate real root is x ≈ 1.32471795
∴ x = 1.32471795
(3x + 4)³ = 2197
Taking the cube root in this case is easier, although we can do it the extended way which is complicated.
![\sqrt[3]{(3x+4)^3}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B%283x%2B4%29%5E3%7D%20)
=
![\sqrt[3]{2197}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B2197%7D%20)
3x + 4 = 13
Now solve normally.
subtract 4
3x + 4 = 13
-4 -4
3x = 9
Divide by 3 to isolate 3

3 and 3 cancels out
x = 3
b is two fifths of c, so we make this a ratio with c = 1.
The ratio of b:c is 2/5 : 1
We also have 4a = 3c, rewrite this ratio so c is 1 by dividing both sides by 4,
so we get the ratio of a to c as 3/4 : 1
Now we get the a:b:c ratio of 3/4 : 2/5 : 1 now we can change the fractions to whole numbers, first by multiplying the 3 numbers by 4 to get get rid of the denominator of 4 in a:
3 : 8/5 : 4
Now multiply the 3 numbers by 5 to remove the denominator of 5 in b:
15 : 8 : 20
Now we can check using the equations:
b is 2/5 of c: 20 x 2/5 = 40/5 = 8 This is true.
4a = 3c: 4(15) = 3(20) = 60 = 60, this is also true.
The ratios is 15 : 8: 20