A meteorologist measures the angle of elevation of a weather balloon as 41 degrees. A radio signal from the balloon indicates that it is 1503 m from his location. To the nearest meter, how high above the ground is the balloon?

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23-12-2016
Physics

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A meteorologist measures the angle of elevation of a weather balloon as 41 degrees. A radio signal from the balloon indicates that it is 1503 m from his location. To the nearest meter, how high above the ground is the balloon?

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Lampa20 Lampa20 · Answer 1 · 2016-12-29T18:58:21+01:00

This problem we can represent as right triangle where we can use basic trygonometric functions.

in this case we have largest side (hypothenuse) of the triangle and we have one angle. The angle we got is the one between side of triangle that is horizontal with the ground and the hypothenuse, meaning that we need sin function to connect relation between angle, known side lenght and unknown side lenght.

sin(alpha) = (side of triangle oposite from observed angle)/(hypothenuse)

sin(41) = x/1503

x = 1503*sin41 = 986.06 meters

Answer is 986.06 meters