Question

One formula used by surveyors to determine the distance between two points is d = 0.5b cos(0.5a) / sin(0.5a), where b is the length of the subtense bar, and a is an angle measured. If the length of the subtense bar is 6 meters, and a = 1.3 degrees, find d. Round your answer to the nearest tenth of a meter.

A. 36.9 meters
B. 45.2 meters
C. 26.1 meters
D. 16.5 meters

Answer 1

To calculate the distance d using the provided formula, substitute the given angle a after converting it to radians and the subtense bar length b into the formula, then compute using trigonometric functions and round to the nearest tenth of a meter, resulting in 26.1 meters.

Step-by-step explanation:

To find d, the distance between two points using the given formula d = 0.5b cos(0.5a) / sin(0.5a), we need to substitute the values of b and a that are given. In this case, b = 6 meters, and a = 1.3 degrees. First, convert angle a to radians because trigonometric functions in calculators typically require angle measurements in radians:

• 1 degree = π/180 radians
• a in radians = 1.3 × (π/180) radians

Then substitute the value of a in radians and b into the formula:

1. 0.5a in radians = 0.5 × 1.3 × (π/180)
2. cos(0.5a) = cos(0.5 × 1.3 × (π/180))
3. sin(0.5a) = sin(0.5 × 1.3 × (π/180))
4. d = 0.5 × 6 × cos(0.5 × 1.3 × (π/180)) / sin(0.5 × 1.3 × (π/180))

Calculate d using a calculator and round to the nearest tenth of a meter:

d ≈ 26.1 meters

The correct answer is therefore C, 26.1 meters.