The altitude of an aeroplane is 500 metres, and the angle of elevation from the runway to the aeroplane is 15^(@). Find the horizontal distance from the aeroplane to the runway, to the nearest centimetre.

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Given Data: Given: Altitude of aeroplane (h) = 500 meters Angle of elevation (θ) = 15 degrees We need to find the horizontal distance (d) from the aeroplane to the runway. We will use the trigonometric relation tan(θ) = opposite/adjacent, where the opposite side is the altitude and the adjacent side is the horizontal distance we want to find.Convert to Radians: First, we need to express the angle of elevation in radians because some calculators require angles in radians for trigonometric functions. However, since we are using the tangent function, and most modern calculators can work with degrees, we can skip this step and directly use the angle in degrees.Apply Tangent Function: Now, we apply the tangent function to the angle of elevation to find the horizontal distance. tan(θ) = h/d tan(15 degrees) = 500/dSolve for Horizontal Distance: We solve for d by rearranging the equation: d = h / tan(15 degrees)Calculate Horizontal Distance: We calculate the horizontal distance using the given altitude and the tangent of 15 degrees: d = 500 / tan(15 degrees)Convert to Centimeters: Using a calculator, we find the value of tan(15 degrees) and then divide 500 by this value to find d. d ≈ 500 / 0.26795 (value of tan(15 degrees)) d ≈ 1865.438 metersRound to Nearest Centimeter: The question asks for the distance to the nearest centimeter, so we convert meters to centimeters by multiplying by 100. d ≈ 1865.438 meters * 100 centimeters/meter d ≈ 186543.8 centimetersWe round the distance to the nearest centimeter. d ≈ 186544 centimeters

The altitude of an aeroplane is $500$ metres, and the angle of elevation from the runway to the aeroplane is $15^{\circ}$ . Find the horizontal distance from the aeroplane to the runway, to the nearest centimetre.

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The altitude of an aeroplane is 500500500 metres, and the angle of elevation from the runway to the aeroplane is 15∘ 15^{\circ} 15∘. Find the horizontal distance from the aeroplane to the runway, to the nearest centimetre.

The altitude of an aeroplane is $500$ metres, and the angle of elevation from the runway to the aeroplane is $15^{\circ}$ . Find the horizontal distance from the aeroplane to the runway, to the nearest centimetre.