78° = acute angle
144° = obtuse angle
229 = 2.29 x 10^2
750 = 7.5 x 10^2
No prob......!!!!
" An approximate solution can be obtained quickly by noting that when theta is small then sin(theta) ≈ theta - theta^3/3!'
Note : Alan derives this from the first two terms of the Taylor Series for the sine function :
sin x = x − x 3 3! + x 5 5! − x 7 7! + x 9 9! − ....
230 = 2.3 x 10^2
5601 = 5.601 x 10^3
14 100 000 = 1.41 x 10^7
56 million = 56 000 000 = 5.6 x 10^7
2/10 = .2 = 2 x 10^(-1)
0.089 = 8.9 x 10^(-2)
0.000 26 = 2.6 x 10^(-4)
0.000 000 698 = 6.98 x 10^(-7)
12 thousandth = .012 = 1.2 x 10^(-2)
5 = 50 - 2x2 add 2x2 to both sides, subtract 5 from both sides
2x2 = 45 divide both sides by 2
x2 = 45/2 take pos/neg roots of both sides
x = ± √ (45/2) = ± √ [ (9 * 5) / 2 ] = ± 3√(5/2) = ± (3/2)√10
Assuming that the first row is "Row 0 "..... the 5th number in row 50 will be given by the combinatoric C(50, 4) = 230.300
Here is a pic of the triangle :
The three altitudes are DC = 8 , AE and BF = 9.6
And the sum of these = 8 + 2(9.6) = 27.2
[66+ 2/3]% = 2/3
So......let N be the total crew........and....
(2/3) N = 8 multiply both sides by 3/2
N = 8 (3/2) = 12 total in the crew
8/5 = 1 + 3/5 = 1 + 6/10 = 1.6
The three altitudes are DC = 8 , AE and BF = 9.6