Question

Construction workers planned to secure a tal pole using two cables attached to the pole at a point 12m above the ground as shown in the diagram below. Based on the information in the diagram, what value represents the total length of the cable that is needed to secure the pole? Round to the nearest hundredth. 12 m 45° 200

Answer 1

The total length of the cables is equal to the sum of the hypotenuses of each right angle.

For the first triangle (on the left, the smaller one) we have to apply the trigonometric function:

Sin β = opposite side / hypotenuse

Where:

β= angle

opposite side = 12

Replacing:

Sin 45 = 12/ h1

Solve for h1

h1= 12/sin45

h1= 16.97m

Same process for the big triangle:

Sin 30 = 12/h2

h2 = 12/Sin30 = 24 m

Add both lenghts:

h1+h2= 16.97+24 = 40.97 m