Question

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Answer 1

The minimum length of the cable needed to connect A and C is = 67.7m

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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