A surveyor,standing 30ft from the base of a building,measures the angle of elevation to the top of the building to be 75 degree.How accurately must the angle be measured for the percentage error in estimating the height of the building to be less than 4%?
Hello, turkeyy!
A different interpretation . . . a different approach.
The wording is somewhat vague.A surveyor, standing 30ft from the base of a building,
measures the angle of elevation to the top of the building to be 75°.
How accurately must the angle be measured for the percentage error
in estimating the height of the building to be less than 4%?
I will assume that 75° is the exact angle of elevation.
Let = the exact height of the building.
We have: . .[1]
Suppose he measures an angle of elevation of degrees.
Then his estimated height is: . .[2]
Divide [2] by [1]: .
is the ratio of the estimated height to the exact height.
. . We want this to be between 96% and 104%.
. .
Therefore, the angle must be measured to ±0.5°.