Trigonometry

A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 58°. A guy wire is to be attached to the top of the tower and to the ground, 50 m downhill from the base of the tower. The angle α in the figure is determined to be 9°. Find the length of cable required for the guy wire. (Round your answer to the nearest meter.)

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  1. without the figure, I can't be certain, but I am vislualizing a hill with a tower, the hill slopes downl, and at 50m slant distance from the tower, with a cable guy at an angle of 9deg to the slope.

    Now on language, the angle of inclination of the hill (measured to the horizontal) is 58, so the angle of depression is 58, so the angle beween the tower and the hill is 90+58 deg

    So I see two angles, and included side, finding the guy wire side

    Now notice the angle of the guy to the tower at the top, 180-9-148=23 check that

    law of sines
    Length/sin148=50/sin23

    solve for length

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    bobpursley
  2. 158

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