Asurveying team set up some equipment 104104 ft from the base of a tree in order to sight the top of the tree. from ground level, they measure the angle of elevation to be 27.5∘27.5∘. if the calculated height needs to be accurate to within 1.51.5%, what is the allowed error in the angle measurement? (assume the 104104 ft measurement is 100% accurate.)

Relative error = 0.0254 %

Step-by-step explanation:

Given details

Height of equipment from base is 104 ft

Elevation angle is 27.5 degree

From figure we have

.........1

x  = 54.13 ft

differentiating 1st eq wrt x

Taken for minute change

from

Reltaive error

Relative error = 0.0254 %

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)