Question

Question #63017

Answer 1

`"distance" = 54.6` `"m"`

Explanation:

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"`