Answer:
Approximately 43 feet of minimum cable is needed.
Step-by-step explanation:
This problem can be solved using Trigonometry and Pythagorean theorem. Pythagorean theorem applies on right-triangles (which are known to have one 90° angle). The theorem states that the square of the Hypotenuse is obtained by the squared sum of the other two sides of the triangle (i.e the two sides forming the 90° angle - with the hypotenuse side being across it as:
[tex]h^2=a^2+b^2[/tex] Eqn. (1)
where
[tex]h[/tex] is the hypotenuse
[tex]a[/tex] is a side
[tex]b[/tex] is a side
Now in this case, the utility pole must be perpendicular to the ground and the anchor being parallel to the ground, and a 90° angle formed between them. Conclusively the cable length will be represented by the hypotenuse in a right triangle. So here we have [tex]a=40ft[/tex] and [tex]b=15ft[/tex]. Plugging in Eqn.(1) and solving for [tex]h[/tex] we have:
[tex]h^2=40^2+15^2\\h=\sqrt{40^2+15^2} \\h=\sqrt{1600+225}\\ h=\sqrt{1825}\\ h=5\sqrt{73}\\ h=42.72ft[/tex]
So we conclude that the minimum length of cable needed by Lamont is
≈43 feet (rounded up).
