Question

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 0° and sights surveyor b. then surveyor a uses the clinometer to sight the cable. at this point, surveyors a and b determine the distance between them to be 17.4 ft (see figure). surveyor a then uses the clinometer to sight surveyor b at the base, a distance of 2.0 ft above the ground. determine the ground clearance of the electrical cable. ground h₂ = 22 45° b h₁ =?

Explanation:

Step1: Analyze the right - triangle

We have a right - triangle formed by the height of the cable above the ground, the horizontal distance from the surveyor to the point directly below the cable, and the line - of - sight from the surveyor to the cable. The angle of elevation is 45°. In a right - triangle, if the angle of elevation $\theta = 45^{\circ}$, and we know that $\tan\theta=\frac{opposite}{adjacent}$. Here, $\tan45^{\circ}=1$, and the horizontal distance (adjacent side) between surveyor A and B is $d = 17.4$ ft. Let the height of the cable above surveyor B be $h_1$.
Since $\tan45^{\circ}=\frac{h_1}{17.4}$, and $\tan45^{\circ}=1$, we have $h_1 = 17.4$ ft.

Step2: Calculate the ground clearance

The total height of the cable above the ground $h$ is the sum of the height of surveyor A above the ground ($h_2 = 2.0$ ft) and $h_1$. So $h=h_1 + 2.0$.
Substitute $h_1 = 17.4$ ft into the formula: $h=17.4+2.0=19.4$ ft.

Answer:

$19.4$ ft