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--------------------------------------------------------------------- practical trigonometry heights and distanceA vertical tree is partially broken by the wind . The top of the tree still connected to the lower portion touches the ground and makes an angle 30 degrees with the ground. If the top of the tree touches the ground 30 m away from the foot of the tree, what was the height of the tree before it broke CAB = full tree broken at A C = top of the tree now touching the ground B = foot of the tree tan(30 degrees) = AB/CB 1/[sqrt(3)] = AB/30 AB= 30 / sqrt(3) introduce conjugate AB = 30*sqrt(3) / 3 = 10*sqrt(3) m --------(1) cos(30 degrees)= BC/AC [sqrt(3)]/2 = 30 / AC AC = 30*2/[sqrt(3)] introduce conjugate AC= 60sqrt(3)/3 = 20*sqrt(3) m ----------(2) Total height of the tree before it broke = AB+AC = 10*sqrt(3)+20*sqrt(3) =30*sqrt(3) m --------------problem 2 Find the sum of all 3 digit natural numbers which are divisible by 8 The smallest 3 digit number is 100 dividing 100 with 8, quotient is 12 with remainder 4 therefore 13*8 =104 is the first term Similarly dividing 999 with 8 quotient is 124 with remainder 7 124*8 = 992 is the last term series is 104 + 112 + ...+992 a = 104 l=992 d=8 (common difference) number of terms n = [(l-a)/d]+1 n = [(992-104)/8]+1=112 sum = [n/2][a+l] =[112/2]*[104+992]=61376 other questions and problems: * integral
calculus integration formula---------------------------------------------------------------------------------------------- trigonometric
identity and ratio of certain standard angles* list
of differentiation formula
*integral
calculus integration formula--------------------------------------------------------------------------------------- |

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