The PLDT has a 183 m straight vertical tower. There are two cables in the same vertical plane anchored at two points on a level with the base of the tower. The angle made by the cables with the horizontal are 44 degrees and 58 degrees, respectively. Find the distance between anchor points if they lie on the same side.
Question
The PLDT has a 183 m straight vertical tower. There are two cables in the same vertical plane anchored at two points on a level with the base of the tower. The angle made by the cables with the horizontal are 44 degrees and 58 degrees, respectively. Find the distance between anchor points if they lie on the same side.
Solution
To solve this problem, we will use the tangent function from trigonometry. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
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First, let's denote the distance from the base of the tower to the closer anchor point as x and the distance from the base of the tower to the farther anchor point as y.
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From the problem, we know that the tower is 183 m tall. So, we can write two equations using the tangent function:
tan(44) = 183/x and tan(58) = 183/y
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Solving these equations for x and y gives:
x = 183/tan(44) and y = 183/tan(58)
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The distance between the two anchor points is then y - x.
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Calculate the values:
x = 183/tan(44) ≈ 225.97 m y = 183/tan(58) ≈ 130.07 m
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Subtract x from y to find the distance between the two anchor points:
y - x = 130.07 m - 225.97 m = -95.9 m
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Since distance cannot be negative, we take the absolute value to get the distance between the two anchor points as 95.9 m.
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