Question

From a point 300 feet above ground in a firetower, a ranger spots two fires in the George Washington National forest. The angle of depression made by the line of sight from the ranger to the first fire is 3oand the angle of depression made by the line of sight from the ranger tothe second fire is 2o. The angle formed by the two lines of sight is 0117. Find the approximate distance between the two fires.

Answer 1

Answer:

The answer is "$\bold{17456.6 \ ft}$"

Step-by-step explanation:

Please find the complete question in the attached file.

$\sin \theta = \frac{P}{h}\\\\\to BC =x\\\\\to BD =y$

The height of tower (AB) = 300 ft

Distance = CD

$\Delta ABC \\\\\sin \theta = \frac{AB}{AC}\\\\\sin (2.5) = \frac{300}{AC}\\\\Ac= \frac{300}{\sin (2.5)}\\\\AC= 6877.68 \\\\\Delta ABD \\\\\sin \theta = \frac{AB}{AD}\\\\\sin (1.3) = \frac{300}{AD}\\\\AD= \frac{300}{\sin (1.3)}\\\\AC= 1322.33$

calculating CD :

$CD^2 = AC^2 +AD^2 -2\cdot AC \cdot AD \cdot \cos(117^{\circ}) \\\\CD = \sqrt{(6877.68)^2 +(13223.23)^2 -2\cdot (6877.68) \cdot (13223.23) \cdot \cos(117^{\circ})}\\\\CD =\sqrt{47302482.1824 + 174853811.6329 - 82576463.207}\\\\CD= \sqrt{304732757.02}\\\\CD= 17456.6 \ ft$