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Pls help WILL GIVE BRAINLIST
A person looking out a window, 40 feet above street level can sight the top and

bottom of the building. The angle of elevation to the top of the building is 61 degrees and the angle

f depression to the bottom of the building is 37 degrees. How tall is the building that the person is looking at

Respuesta :

Answer:

135.94 feet

Step-by-step explanation:

Split the problem into two parts :

  1. Distance between viewer and building
  2. Height of the top part of the building

Distance between viewer and building

  • The lower part of the building is 40 feet, as it is mentioned the viewer is 40 feet above street level
  • Let the distance be called 'd'
  • Therefore, tan37° = 40/d
  • tan37° = 3/4 = 0.75
  • ⇒ 40/d = 0.75
  • ⇒ d = 40/(3/4) = 40 x 4/3 = 160/3 = 53.3 feet

Height of the top part of the building

  • Let the height of the top part be 'h'
  • Therefore, tan61° = h/d = h/53.3
  • tan61° = 1.8
  • ⇒ h/53.3 = 1.8
  • ⇒ h = 53.3 x 1.8 = 95.94 feet

Total height of building

  • Lower part + Top part
  • 40 + 95.94
  • 135.94 feet