What is the length of the guy wire?

Question

A guy wire to the top of a tower makes an angle of 61 degrees with the level ground. At a point 28ft farther from the base of the tower and in line with the base of the wire, the angle of elevation to the top of the tower is 30 degrees. What is the length of the guy wire?

Answer 1

this is a classic trig application problem.

draw a line segment horizontally on paper passing from point A through point B on to point C, the base of the tower.

draw a perpendicular at C, to endpoint D (above C).

draw AD; draw BD.

label angle DAC = 30 degrees

label angle DBC 62 degrees.

label AB = 28; label BC = x.

 

tan 62 = DC/x  (DC is height of tower)

tan 30 = DC/(28+x)...Equation II.

 

solve for x from the first equation above: x = DC/tan 61.

substitute for x in equation II.  you now will have an equation involving DC and numbers (including decimal values for tangents).  I leave it to you to complete the task...DC occurs in two places so you will have to use algebra skills from here on.

 

Also: check your answer, when completed. I recommend using tangent values to 5 decimal places during the calculation, for accuracy of final result.