Answer to Question #300059 in Trigonometry for Ravneet

Question

Fire tower A is x = 29 kilometers due west of tower B. A fire is spotted from the towers, and the bearings from A and B are 𝜃 = N 78° E and φ = N 54° W, respectively (see figure). Find the distance d of the fire from the line segment AB. (Round your answer to two decimal places.)

Answer 1

Let F is the point where the fire is.$\angle A= 90^°-78^°=12°$

$\angle B= 90^°-54^°=36°$

$\angle F = 180^°-(12^°+36^°)= 132°$

$\frac{29}{sin132°}=\frac{FA}{sin 36^°}$

$FA=22.94$

Area of $\triangle FAB= ½(22.94)(29)sin12^°=½×29×h$

$h=4.7695$