# Math Help - Trig Word Prob- how wide is the fire?

1. ## Trig Word Prob- how wide is the fire?

hey just wondering if anyone can figure out the following problem...

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 degrees and the other makes an angle of depression of 85 degrees on the other side of the helicopter, how wide is the fire?

Thanks in advance..its been troubling me

2. 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 $H\!:\;\;HC = 300$

$\begin{array}{ccc}\angle WHA = 40^o = \angle HAC & \Rightarrow & \angle AHC = 50^o \\
\angle EHB = 85^o = \angle HBC & \Rightarrow & \angle BHC = 5^o \end{array}$

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

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

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

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

3. thanks that helped alot...i never thought to draw a picture