A forest ranger is watching the progress of a forest fire sp

A forest ranger is watching the progress of a forest fire spreading towards her from the top of a 3775-foot mountain. In 6 minutes, the angle of epression to the leading edge of the fire changed from 0.73 radians to 1.15 radians. How many feet does the fire advance during the 0 minutes the ranger observed the fire? feet Preview Al what speed (in feet per minute) is the fire spreading towards the ranger? feet per minute Preview

Solution

Here the difference between two angles =1.15 -0.73 = 0.42 radian

Now in such right triangle,

tan A= height/base

or tan 0.42 = 3775/b

or 0.4465 =3775/b

or b = 3775/0.4465 = 8453

so fire advances by 8453 feet.

This is the first answer.

And as this distance is covered in 6 minutes, so its speed = 8453/6 =1409 feet/min

This is the second answer.