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the Angle of depression of a stone on the ground from the top of a tower is 45. if the stone is at a distance of 120 meters away from the building, find the height of the tower.​

Sagot :

KAntoineDoix

ANGLE OF DEPRESSION

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» The location of the stone (C) is 120 meters (a) away from the foot of the tower (B). The angle of depression of the stone is 45° from the top of the tower (A). Hence, we need to create a Right Triangle to find the height of the tower (c).

» The horizontal line is perpendicular to the line from the bottom of the tower to the sky. Thus, the angle of the depression and the angle (x) between the wall of the tower and the line of displacement from the top of the tower to the stone are complementary (having a sum of 90°). Find the measure of (x)

  • x + 45° = 90
  • x = 90° - 45°
  • x = 45°

[tex] \: [/tex]

Given:

  • Angle A = 45°
  • Side (a) = 120m

Find:

  • Side (c)

[tex] \: [/tex]

» And now that we have the given and the "what we need to find". We need to choose a trigonometric ratio to find the height of the tower (c). Let angle A as our reference:

  • Side (a) is the opposite side of A
  • Side (c) is the adjacent side of A

» Since the opposite side and the adjacent side are present to angle A, we are gonna use the tangent ratio (tan).

  • tan θ = opposite/adjacent
  • tan A = a/c
  • tan 45° = 120m/c
  • c = 120m(tan 45°)
  • c = 120m

» Thus the height of the tower is 120 meters.

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