The minimum length of the cable needed to connect A and C is = 67.7m
The distance between the two towers are same.
Calculation of the cable length
The sides of the triangle can be determined using the law of cosine. That is,
Sin A/a = Sin C/c
There are three triangles with different sides and angles.
To find the AP side of triangle ABP the cosine triangle is used.
SinA = <APB = Sin 50°
a = 30m
SinC= <ABP= sin 90°
c = X
X= sinC *a/SinA
X= 1*30/0.7660
X= 39m
But < APC = 180( 50+35)
= 180 - 85 = 95°
Since < CPD = 35° = < ACP
Using the cosine rule,
Sin A = <APC = 95°
a = AC = X
Sin C = 35°
c = 39
X = Sin 95°× 39/sin 35°
X= 0.996*39/0.5736
X = 38.844/0.5736
X= 67.7m
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