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practical trigonometry

heights and distance
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practical trigonometry heights and distance
A student sitting in a classroom sees a picture on
the black board at a height of 1.5m from the horizontal
level of sight. The angle of elevation of the picture
is 30 degrees. as the picture is not clear to him he
moves straight towards the black board and sees the
 picture at an angle of elevation 45 degrees. Find the
distance moved by the student
practical
                  trigonometry heights and distance

Let A = position of the picture
C = original position of the boy
M = new position of the boy

from triangle ABC
tan(30degree)=AB/BC
1/[sqrt(3)]=1.5/BC
therefore BC=1.5*sqrt(3 ) m----------(1)


from triangle ABM
tan(45degree)=AB/BM
1 = 1.5/BM
therefore BM = 1.5 m-----(2)

from diagram
CM =BC-BM =
1.5*sqrt(3 )-1.5
=1.5[sqrt(3)-1] =1.5[1.732-1]=1.5*0.732
=1.098 m
Distance moved by the boy = 1.098 m


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problem 2
  A ladder leaning against a vertical wall
makes an angle of 60 degrees with the ground.
The foot of the ladder is 3.5 m away from
the wall. Find the length of the ladder

height and distance
let
AC = ladder
AB = wall
cos(60 degree) = BC / AC
[1/2] = 3.5/AC
AC = 3.5*2 = 7 m
Length of the ladder 7m


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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