# Question 63017

Jul 17, 2017

$\text{distance} = 54.6$ $\text{m}$

#### 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 $10$ $\text{s}$ going at a constant speed of $5$ $\text{m/s}$ is

(5"m"/(cancel("s")))(10cancel("s")) = 50 $\text{m}$

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

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

$50$ $\text{m}$ $- 1.8$ $\text{m}$ $= 48.2$ $\text{m}$

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

$\sin \frac{{62}^{\text{o") = (48.2color(white)(l)"m}}}{x}$

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