Explanation:
so, we have a right-angled triangle.
the line of sight (top of the tower to the fire in the ground) is the Hypotenuse (the baseline opposite to the 90° angle).
the tower itself (180 ft) and the ground distance (from the base of the tower to the fire) are the legs enclosing the 90° angle.
the angle of depression (20°) at the top of the tower is the same as the angle of elevation at the point of the fire looking up to the tower.
then we know the 90° at the base of the tower.
and the third inner angle (at the top of the tower) is then
90 - 20 = 70°.
remember the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
where the sides (a, b, c) are always opposite to the correlated angles (A, B, C).
so, in our case we have
180/sin(20) = distance/sin(70)
distance = 180×sin(70)/sin(20) = 494.5459355... ≈
≈ 495 ft