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A utility pole is supported by two wires, one on each side, going in the opposite direction. The two wires form a 75-degree angle at the utility pole. if the wires are 12 meters and 16 meters long and secured to the ground, find the distance between the wires on the ground.

 Feb 13, 2020
 #1
avatar+109740 
+1

The wires form the hypotenuses of two right triangles.....we need the distance in each case of the opposite side to the 75° angles

 

sin (75)  =   distance1 / 12

sin (75)  =   distance 2 / 16

 

 

So....We can find the distance thusly :

 

(12 + 16) sin (75)  =   distance1 + distance2

 

28sin(75) ≈ 27.05 ft

 

cool cool cool

 Feb 13, 2020
 #2
avatar+22108 
+2

The two wires form a 75 degree angle at the pole

 

 

Law of Cosines    c2 = a+ b2  - 2 a b cos 75       c is the distance we are looking for in the Q    a = 12   b = 16

                                 = 12^2 +16^2 - 2 (12)(16) cos 75

                              c^2 = 300.61

                               c = 17.33 Meters   betwen the wire anchors at the ground

 Feb 13, 2020

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