Question

3. Two fire towers are 30 kilometers apart, tower A being due

west of tower B. A fire is spotted from the towers, and the

bearings from A and B are E 14° N and W 34° N, respectively.

Find the distance d of the fire from the line segment AB.

Answer 1

Answer:

Step-by-step explanation:

From the attachment we have a triangle ABD, but sum of angle in a triangle is 180 which means angleABD=180

Angle A=14

Angle B= 34

Then angle D= 180-(14+34)=132deg.

From trigonometry

a/sinA=b/sinB = c/sinD

a/sin14 = b/sin34= 30/sin132

But sin(14)=0.991

Sin(132)= 0.0531

Then substitute we have

a/0.991 = 30/0.0531

Then cross multiply we have

0.0531×a=30× 0.991

a= 29.73/0.0531

a=9.77km

Therefore, the distance d of the fire from the line segment AB is 9.77km