Problema Solution
Trigonometry question
A vertical pole is anchored by two cables on the same side. the two poles are attached to the top of the [pole.The angles of elevation from the anchor points on the ground to the top of the pole are 18° and 28°. the distance between the anchor points is 11meter calculate the lengths of the cables and the height of the poles
Answer provided by our tutors
First we make a good drawing:
AP and BP are the lengths of the cables
h is the height of the pole
tan(18) = h/(11 + x)
h = (11 + x)*tan(18)
tan(28) = h/x
h = x*tan(28)
We have the following system of equations:
tan(18) = h/(11 + x)
tan(28) = h/x
........
click here to see the system of equations solved for h and x
........
h = 9.19 m
x = 17.28 m
Next, we will use the Pythagorean Theorem to find AP and BP:
AP^2 = (11 + x)^2 + h^2
AP^2 = (11 + 17.28)^2 + 9.19^2
AP = 29.74 m
BP^2 = h^2 + x^2
BP^2 = 9.19^2 + 17.28^2
BP = 19.57 m
The lengths of the cables are: 29.74 m and 19.57 m.
The height of the pole is 9.19 m.