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practical trigonometry

heights and distance
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practical trigonometry heights and distance


The angle of elevation of the top of a hill from
the foot of a tower is 60 degrees and the angle of
elevation of the top of the tower from the foot of the hill
is 30 degrees. If the tower is 50 m high find the
height of the the hill

heights and distance
let TO =tower
HI =hill

from triangle OHI
tan(30 degrees )= HO /IO
1 / [sqrt(3)] = 50 / IO
IO =50 sqrt(3) m ----------(1)

from triangle HIO
tan(60 degrees) =HI/ IO

sqrt(3) =HI / [50 sqrt(3)] using equation(1)

HI = 50*sqrt(3)*sqrt(3)
HI = 150 m



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problem 2
  

P and Q trisect the line segment joining
(2,1) and (5,-8). If P lies on 2x-y+k=0
find the value of k

P divides the line segment joining
(2,1) and (5,-8) in the ratio 1:2 internally
 while Q will divide the same line
segment in the ratio 2 :1 internally
Using section formula
 [formulae on analytical geometry]
P=( [1*5+2*2]/[1+2] , [1*(-8)+2*1]/[1+2] )
P=( 3 , -2)
given that P(3,-2) lies on 2x-y+k=0
therefore
2*3-(-2)+k=0
8+k=0
k=(-8)


other questions and problems:


*integral calculus integration formula





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trigonometric identity and ratio of  certain standard angles

*list of differentiation formula     *integral calculus integration formula
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