Question #63017

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Answer 1 · 2017-07-17T21:47:44

$"distance" = 54.6$ $"m"$

We're asked to find how far Sam's head is from the helicopter, with some given measurements.

The helicopter is supposedly traveling vertically upward, and its position after $10$ $"s"$ going at a constant speed of $5$ $"m/s"$ is

$(5"m"/(cancel("s")))(10cancel("s")) = 50$ $"m"$

The angle of elevation from Sam to the helicopter at this time is given as $62^"o"$ . (I'll assume this angle is taken from his head height.)

We also know Sam's height is $1.8$ $"m"$ , so the vertical distance from Sam's head to the helicopter is

$50$ $"m"$ $- 1.8$ $"m"$ $= 48.2$ $"m"$

Using trigonometry, we can find the hypotenuse of the right triangle created in this problem:

$sin(62^"o") = (48.2color(white)(l)"m")/x$

$x = (48.2color(white)(l)"m")/(sin(62^"o")) = color(red)(54.6$ $color(red)("m"$