Question

A surveying team set up some equipment 110 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 25°, if the calculated height needs to be accurate to with 2%, what is the allowed error in the angle measurement

Answer 1

Explanation:

Distance from equipment position to tree base is known. Measured angle of elevation is twenty five degrees. What is the allowed error in the angle measurement?

Two percent of twenty five degrees is

2/100 × 25 = 0.02 × 25 = 0.5

This is the allowed error in the angle measurement - 0.5 degrees

Hence, the angle could or should fall anywhere between 24.5 and 25.5

These two figures are gotten by subtracting 0.5 from 25 and by adding 0.5 to 25 respectively.

The allowed error in the angle measurement is 0.5 degrees.