In a circus, a guy wire A is attached to the top of a 30-ft pole. Wire B is used for performers to walk up to the tight wire, 10 ft above the ground. Find the angle ϕ between the wires if they are attached to the ground 40 ft from the pole.

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Daphne Broadhurst · Accepted Answer

Let x be the angle of the smaller right triangle and y be the angle of the larger right triangle so that: ϕ=y−x For the smaller right triangle with hypotenuse as guy wire B, we can use the tangent ratio to find x: tan⁡x=1040 x=tan−1(1040) x∼14.04° For the larger right triangle with hypotenuse as guy wire A, we can use the tangent ratio to find y: tan⁡y=30+1040 tan⁡y=1 y=tan−1∗1 y=45∘ Hence, ϕ=45°−14.04° ϕ≈30.96°

In a circus, a guy wire A is attached to the top of a 30-ft pole. Wire B is used for performers to walk up to the tight wire, 10 ft above the ground.

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