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The position of the top corner of the le...

The position of the top corner of the lecture room was required. To find this a theodolite was
set up as in the figure below. The distance to the side wall, along the x-axis is 7 m, and following
angles were measured `AOX = 60^(@), AOY= 45^(@)` Calculate the coordinates of the corner realtive
to the position of theodolite.

Text Solution

Verified by Experts

`l=x/r = cos 60^(@) = 0.5`
`m=y/r=cos 45^(@) = 1/sqrt(2)`
using
`l^(2) + m^(2) + n^(2)= 1`
`1/4+1/2 + n^(2) =1`
`n^(2) = 1/4`
`n=pm 1/2`
`cos gamma=+1/2 rArr gamma = 60^(@)`
Length OA can be calculated as
`x/r =0.5`
`r= 7/(0.5)=14`
Fron the other direction cosines
`y=14 cos beta = 14 xx 1 /(sqrt(2))=7sqrt(2)`
`z = 14 cosgamma = 14 xx 1/2 =7`
Coordinates of corner `=(7, 7sqrt(2), 7)`.
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