From a point on the ground a person notices that a 75foot antenna on the top?

Question

of a building has an angle of elevation of 65 . If the angle of elevation to the top of the building is 50^degree, How tall is the building?

Answer 1

Right angled triangle ABC right angled at B
/_ C = 50°
AB = h is height of building.
BC = x
D lies on AB produced such that AD = 75
/_DCA = 15°

tan 50° = h/x
h = x tan 50°
x = h / tan 50°

Tan 65° = (75 + h) / x
x = (75 + h) / tan 65°

h / tan 50° = (75 + h) / tan 65°
tan 65° h = tan 50° (75 + h)
(tan 65° - tan 50°) h = 75 tan 50°
h = 75 tan 50° / (tan 65° - tan 50°)
h = 93.8 ft

Answer 2

let h = height of building...
x = distance of person from the base of the building...

then
tan(65°) = (75+h)/x
tan(55°) = h/x

x =(75 + h) / tan(65°) = h / tan(55°)

thus
tan(55°) (75+h) = tan(65°) h
h = [75tan(55°)] / [tan(65°) - tan(55°)] feet
≈ 149.52 feet

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Answer 3

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