Need help with this problem! Thanks in advance.
The ground clearance of an overhead electrical cable must be determined. Surveyor B is
positioned directly under the cable (surveyor B can make a position check by sighting
past the string of a plumb bob, held in his or her outstretched hand, to the cable); surveyor A sets the clinometer to 45°and then backs away from surveyor B until the over-
head electrical cable is on the cross-hair of the leveled clinometer. At this point,surveyors A and B determine the distance between them to be 36.5 ft (see figure). Surveyor A then sets the clinometer to 0°and sights surveyor B; this horizontal line of sight
cuts surveyor B at the knees, a distance of 2.2 ft above the ground.
Determine the ground
clearance of the electrical cable, show your work.
The clinometer shows 45°, so for an isosceles triangle, the horizontal and vertical distances are the same, namely 36.5 ft.
The clinometer is at the same level as surveyor's knees, namely 2.2 ft. above ground level.
The ground clearance is therefore the sum of the two.
Note: it is extremely dangerous to try to
38.7
To determine the ground clearance of the electrical cable, we need to break it down into two components - the vertical distance from Surveyor B to the cable and the vertical distance from the cable to the ground.
Let's start by calculating the vertical distance from Surveyor B to the cable using the clinometer reading of 45°.
1. First, we need to calculate the horizontal distance between Surveyor A and the cable. This can be achieved by using the trigonometric relationship between the horizontal and vertical distances in a right triangle.
The horizontal distance is given as 36.5 ft.
2. Now, we can calculate the vertical distance from Surveyor B to the cable using trigonometry. Since Surveyor A set the clinometer to 45°, we can use the tangent function.
tan(45°) = (vertical distance) / (horizontal distance)
Rearranging the equation, we get:
(vertical distance) = tan(45°) * (horizontal distance)
Substitute the values:
(vertical distance) = tan(45°) * 36.5 ft
Calculate the value of tan(45°) using a calculator:
(vertical distance) = 1 * 36.5 ft
(vertical distance) = 36.5 ft
So, the vertical distance from Surveyor B to the cable is 36.5 ft.
Next, we need to calculate the vertical distance from the cable to the ground using the clinometer reading of 0°.
1. Surveyor A sets the clinometer to 0° and sights Surveyor B. The horizontal line of sight cuts Surveyor B at the knees, which is a distance of 2.2 ft above the ground.
2. This means that the difference between the cable and the ground is 2.2 ft.
Finally, we can calculate the ground clearance of the electrical cable by adding the two vertical distances previously calculated.
Ground clearance = (vertical distance from Surveyor B to the cable) + (vertical distance from cable to ground)
Ground clearance = 36.5 ft + 2.2 ft
Ground clearance = 38.7 ft
Therefore, the ground clearance of the electrical cable is 38.7 ft.