Trig question!?

Question

A forest ranger in a tower 128m high observes two fires in the same line of sight with angles of depression 42 degrees and 61 degrees . How far apart are the fires.

Answer 1

let A & B are the points on fire
horizontal distance of A = 128 cos 61 = 62.056 m
horizontal distance of B = 128 cos 42 = 95.123 m
distance between A & B = 95.123 - 62.056 = 33.07 meters

Answer 2

Hello,

Let d1 = the distance from tower to the fire at 42 degrees
Let d2 = the distance from tower to the fire at 61 degrees

So Tan 42 = d1/128
Tan 61 = d2/128

then d1 = Tan42*128 = 16.21
d2 = Tan61*128 = 32.47

Now the difference of these two is the distance they are apart. Giving us 16.26 meters.

Hope This Helps!