Verified answer

Answer:

C. 65.89 meters

  (Actually, the answer is 65.33 meters which not among the choices, but that is the closest one)

Step-by-step explanation:

The angle of depression is the angle between a straight horizontal line of sight and a line below that. See attachment 1 - tower.

We can then see that the line of sight (the green line in the picture) and the tower has an angle of 90°, a right angle. We can then have an imaginary rectangle having all right angles on its corners.

Since that is the case, we can conclude that the angle between the line of the fire to the lookout and the line from the fire to the tower is CONGRUENT. See attachment 2 - angles. Basically, they are equal.

Now, we have the angle facing the tower which is 20° 10'22", and the height of the tower which is 24 meters.  See attachment 3 - given. Applying trigonometry, specifically SOH CAH TOA, we will use the formula using tangent.

   tangent =

(We will use tangent because the given is the sides involved are the adjacent -the one we are looking for - and the opposite - the height of the tower.)

So, to find the distance of the fire to the base of the tower:

  We substitute the given and placed x as the missing value.

   tan(20°10'22") =  24 / x

   x = 24 / (tan(20°10'22"))

   x = 65.33 meters

To learn more, see this link

https://www.math-only-math.com/angle-of-depression.html

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