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Una torre de comunicaciones tiene una altura de 50 metros. Desde la base de la torre, un observador ve un ángulo de elevación de 60 grados hasta la parte superior de la torre. Calcula la distancia desde la base de la torre hasta el punto donde se encuentra el observador.

Una torre de comunicaciones tiene una altura de 5050 metros. Desde la base de la torre, un observador ve un ángulo de elevación de 6060 grados hasta la parte superior de la torre. Calcula la distancia desde la base de la torre hasta el punto donde se encuentra el observador.

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Q. Una torre de comunicaciones tiene una altura de 5050 metros. Desde la base de la torre, un observador ve un ángulo de elevación de 6060 grados hasta la parte superior de la torre. Calcula la distancia desde la base de la torre hasta el punto donde se encuentra el observador.
  1. Identify Triangle: Identify the right triangle formed by the tower, the line of sight, and the ground. The tower's height is the opposite side, and the distance we need to find is the adjacent side of the 6060-degree angle.
  2. Use Tangent Function: Use the tangent function, which relates the opposite side to the adjacent side in a right triangle. The formula is tan⁡(θ)=oppositeadjacent\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}.
  3. Plug in Values: Plug in the known values: tan⁡(60∘)=50 metersdistance\tan(60^\circ) = \frac{50 \text{ meters}}{\text{distance}}. We know that tan⁡(60∘)\tan(60^\circ) is 3\sqrt{3}.
  4. Solve for Distance: Solve for the distance: distance=50 meters3\text{distance} = \frac{50 \text{ meters}}{\sqrt{3}}. Simplify the expression.
  5. Calculate Final Distance: Calculate the distance: distance=503≈501.732≈28.87 meters.\text{distance} = \frac{50}{\sqrt{3}} \approx \frac{50}{1.732} \approx 28.87 \text{ meters}.

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