Hey, Need some help working these 3 problems. I have the answers but I'm having problems working them. Thank you in advance.
The slope measurement between two points is 25.333 m and the slope angle is 1°50. Compute the horizontal distance.
A distance of 177.50 ft was measured along a 3% slope. Compute the horizontal
distance.
The slope distance between two points is 29.705 m and the difference in elevation between the points is 3.658 m. Compute the horizontal distance.
horizontal distance=slopemeasurement*cosineTheta
on the final one:
horizontal=sqrt(slope^2 + elevation^2)
Minor correction:
horizontal=sqrt(slope^2 - elevation^2)
mjkkk
Sure, I can help you with these problems. Let's work through each of them step by step:
1. The slope measurement between two points is 25.333 m and the slope angle is 1°50. We need to compute the horizontal distance.
To find the horizontal distance, we can use the formula: Horizontal Distance = Slope Measurement * Cos(Slope Angle)
First, convert the slope angle from degrees to radians. To do this, multiply the angle by π/180:
1°50 * π/180 = 0.0314 radians (approximately)
Next, use the formula to calculate the horizontal distance:
Horizontal Distance = 25.333 m * Cos(0.0314 radians)
Use a calculator to find the cosine of the angle, which is around 0.9995:
Horizontal Distance ≈ 25.333 m * 0.9995 ≈ 25.33 m (approximately)
Therefore, the horizontal distance is approximately 25.33 m.
2. A distance of 177.50 ft was measured along a 3% slope. We need to compute the horizontal distance.
To find the horizontal distance, we can use the formula: Horizontal Distance = Slope Distance / √(1 + Slope Percent^2)
First, convert the slope percent to a decimal by dividing it by 100:
3% = 3 / 100 = 0.03
Next, use the formula to calculate the horizontal distance:
Horizontal Distance = 177.50 ft / √(1 + 0.03^2)
Evaluate the square of the slope percent:
0.03^2 = 0.0009
Then, find the square root of (1 + 0.0009):
√(1 + 0.0009) = √(1.0009) ≈ 1.00045
Finally, calculate the horizontal distance:
Horizontal Distance = 177.50 ft / 1.00045 ≈ 177.45 ft
Therefore, the horizontal distance is approximately 177.45 ft.
3. The slope distance between two points is 29.705 m and the difference in elevation between the points is 3.658 m. We need to compute the horizontal distance.
To find the horizontal distance, we can use the Pythagorean theorem: Horizontal Distance = √(Slope Distance^2 - Elevation Difference^2)
Using the given measurements, we have:
Horizontal Distance = √(29.705 m^2 - 3.658 m^2)
Evaluate the square of the slope distance and the square of the elevation difference:
29.705 m^2 ≈ 882.315 m^2
3.658 m^2 ≈ 13.375 m^2
Then, subtract the square of the elevation difference from the square of the slope distance:
882.315 m^2 - 13.375 m^2 ≈ 868.94 m^2
Finally, find the square root of 868.94:
√(868.94) ≈ 29.47 m
Therefore, the horizontal distance is approximately 29.47 m.
I hope this helps you solve the problems. Let me know if you have any further questions!