Final answer:
To compute the horizontal distance with the given slope angle of 1 degree and 5 minutes, and the slope measurement of 36.255 meters, convert the angle to decimal degrees, and use the cosine function. The horizontal distance is approximately 36.246 meters.
Step-by-step explanation:
The slope angle and the slope measurement between two points are given, and the task is to compute the horizontal distance. The slope angle is 1 degree and 5 minutes; first, we need to convert this angle into decimal degrees. Each minute is 1/60 of a degree, so 5 minutes is 5/60 or 1/12 of a degree. Thus, the angle in decimal degrees is 1 + 1/12, which is approximately 1.08333 degrees.
The slope measurement is the length of the slope, which is the hypotenuse of a right triangle where the horizontal distance is the base, and the vertical distance is the height. To find the horizontal distance, we use the cosine of the slope angle:
Cos(angle) = Adjacent side (horizontal distance) / Hypotenuse (slope measurement). Therefore:
Horizontal distance = Cos(angle) × Slope measurement
= Cos(1.08333 degrees) × 36.255 meters
= 0.9998477411 × 36.255 meters
= approximately 36.246 meters, which is the horizontal distance.