From 2 points on opposite sides of a pole 33m high, the angles of elevation of the top of the pole are53 and 67. if the 2 points and base of the pole are on the same horizontal level ,
ScanSolve AI Answer
Step-by-step solution
5 stepsThe problem statement appears to be incomplete, but it describes a scenario where two points are on opposite sides of a pole, and their angles of elevation to the top of the pole are given. The most common question in such a scenario is to find the distance between these two points. Assuming this is the question:
The distance between the two points is approximately 38.9 meters.
Here's how to calculate it:
Define variables
- Height of the pole (h) = 33 m
- Angle of elevation from point 1 (θ₁) = 53°
- Angle of elevation from point 2 (θ₂) = 67°
- Distance from the base of the pole to point 1 (x₁)
- Distance from the base of the pole to point 2 (x₂)
- Total distance between the two points (D) = x₁ + x₂
Use trigonometry (tangent function)
For a right-angled triangle, tan(angle) = opposite / adjacent.
- For point 1: tan(θ₁) = h / x₁ => x₁ = h / tan(θ₁)
- For point 2: tan(θ₂) = h / x₂ => x₂ = h / tan(θ₂)
Calculate x₁
x₁ = 33 m / tan(53°)
x₁ ≈ 33 m / 1.3270
x₁ ≈ 24.868 mCalculate x₂
x₂ = 33 m / tan(67°)
x₂ ≈ 33 m / 2.3559
x₂ ≈ 13.991 mCalculate the total distance (D)
D = x₁ + x₂
D ≈ 24.868 m + 13.991 m
D ≈ 38.859 mRounding to three significant figures, the distance between the two points is 38.9 meters.
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