Double Trigonomentry

Question

two fire towers are 40 kilometers apart. Tower B is due east of Tower A. A fire is spotted from both towers. From tower A the fire is E 21 degrees North and from Tower B the fire is W 38 degrees North. Find the distance of the fire from the line connecting the towers, to the nearest kilometer

Answer 1

Draw and label a diagram,

Draw a line from the fire to the line connecting the two towers

Label this line d (for distance)

Label the intersection with the road C

tan 38° = d / CB

CB = d / tan 38°

tan 21° = d / CA

CA = d / tan 21°

CA + CB = 40

(d / tan 21°) + (d / tan 38°) = 40

Can you solve for d and answer?