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I need an urgent help with this problem, hope that you can explain to me how.
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From a point 55m up from the ground on a vertical antenna pole, three guy cables are stretched to anchors which are located at the vertices of an equilateral triangle 20m on a side. Find the length of each cable if the foot of the pole is equidistant from the anchors.
The Height on an equilateral triangle is a median.
distance from the foot of the pole to the vertex of the triangle is 2/3 the height. This is one side of a right triangle, the other side is 55 m. Apply Pythagorean teorem; this assumes the cable are perfect straight lines.
Sketch the 3D scenario to help yourself visualize the problem, start by drawing the 3 different triangles which have the vertices:
1) The pole's top, the pole's bottom, one cable guy's position
2) The pole's top, one cable guy's position, another cable guy's position
3) The pole's bottom, one cable guy's position, another cable guy's position
Fill in angles and lengths you know.
Some sides of those 3 triangles are the same as sides in other triangles so use the same symbols for unknown lengths. Combining information from all 3 diagrams you should be able to find unknown lengths and angles