Hello, jstrickland!

Did you make a sketch?

A helicopter is dropping water on a forest fire from a height of 300 feet.

If one side of the fire makes an angle depression of 40° and the other side

makes an angle of depression of 85° on the other side of the helicopter,

how wide is the fire? Code:

H
W - - - - - * - - - - - E
40° * |* 85°
* | *
* 50°|5°*
* | *
* 300| *
* | *
* 40° | 85°*
A * - - - - - - - * - - - * B
: d C e :

The helicopter is at $\displaystyle H\!:\;\;HC = 300$

$\displaystyle \begin{array}{ccc}\angle WHA = 40^o = \angle HAC & \Rightarrow & \angle AHC = 50^o \\

\angle EHB = 85^o = \angle HBC & \Rightarrow & \angle BHC = 5^o \end{array}$

Let $\displaystyle d = AC,\;e = CB$

In $\displaystyle \Delta HCA\!:\;\;\tan 50^o \:=\:\frac{d}{300} \quad\Rightarrow\quad d \:=\:300\tan50^o \:\approx\:357.5 $ ft

In $\displaystyle \Delta HCB\!:\;\;\tan5^o \:=\:\frac{e}{300} \quad\Rightarrow\quad e \:=\:300\tan5^o \:\approx\:26.2$ ft

The width of the fire is: .$\displaystyle 357.5 + 26.2 \:=\:383.7$ ft