Two guy wires support a cell tower. Both guy wires touch the ground in the same place, 14.5 m away from the base of the tower. One guy wire reaches 4.2 m higher up the tower than the other. The shorter guy wire makes a 46° angle with the ground. Determine the angle the other guy wire makes with the ground, to the nearest tenth of a degree.

Question

Mathematics

Xander Hester

5 July, 04:18

Two guy wires support a cell tower. Both guy wires touch the ground in the same place, 14.5 m away from the base of the tower. One guy wire reaches 4.2 m higher up the tower than the other. The shorter guy wire makes a 46° angle with the ground. Determine the angle the other guy wire makes with the ground, to the nearest tenth of a degree.

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Kaiden Mcclure · Answer 1

Ok, so.

You first need to find the height of the shorts guy's setup. We know that the length of the base is 14.5, and that theta is 46 degrees. The opposite side equals tan46 * 14.5, which is 14.935. 14.935 is the height of the short guy's height. Now onto the other dude. We know that the height of his setup is 4.2 more than the shorts guy, which is equal to 19.13. Finally, to find the angle, theta, of the second guy, we take 19.13 / 14.5 and then take the inverse tangent of that number (1.31) which equals approximately 52.6 degrees.