Acell phone tower is anchored by two cables on each side for support. the cables stretch from the top of the tower to the ground, with each being equidistant from the base of the tower. the angle of depression form the top of the tower to the point in which the cable reaches the ground is 23 degrees. if the tower is 140 feet tall, find the ground distance between the cables.

659.64 feet

Step-by-step explanation:

We are given that a cell phone tower is anchored by two cables on each side for support. The cables stretch from the top of the tower to the ground, with each being equidistant from the base of the tower so first of all we have to draw a diagram for this scenario as shown below figure 1

Next we are given that angle of depression from the top of the tower to the point in which the cable reaches the ground is 23 degrees as shown in figure 2

So from here we can conclude that as tower is 140 feet tall and the base angle between cable and ground would be also 23 degrees

so we just the trigonometric identity to find x

tan(theta) = opposite over hypotenuse

we know the angle theta = 23

opposite = 140 ( height of tower)

and base is the distance on one side of tower

so finally tan 23 = 140/x (tan = opposite over adjacent)

doing cross multiplication we get

x = 140 / tan 23  

x = 329.82(rounded to hundredth)

so total ground distance between the cables = 2x = 2(329.82) = 659.64 feet

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

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