From the top of a building 15m high the angle of elevation of top of a tower is 30 degree..from bottom of same building ,angle of elevation of same building is 60 degree..find height of tower and distance b/w tower and building
Answers
Answer:
Height = 22.5 m
Distance = 7.5√3 m
Step-by-step explanation:
Define x:
Let x be the difference in the height of the two building.
Let y be the distance between the two building
Form the first equation:
tan θ = opp/adj
tan(30) = x/y
y tan (30) = x
y = x/tan(30)
y = 3x/√3
Form the second equation:
tan θ = opp/adj
tan(60) = (15 + x)/y
y tan(60) = 15 + x
y = (15 + x)/tan(60)
y = (15 + x)/√3
Equate both y:
3x/√3 = (15 + x)/√3
3x = 15 - x
2x = 15
x = 7.5 m
Find y:
y = 3x/√3
y = 3(7.5)/√3
y = 7.5√3 m
Height of the tower = x + 15 = 7.5 + 15 = 22.5 m
Distance between the two building = y = 7.5√3 m
Answer: Height = 22.5 m, Distance = 7.5√3 m
Answer:Answer:
Height = 22.5 m
Distance = 7.5√3 m
Step-by-step explanation:
Define x:
Let x be the difference in the height of the two building.
Let y be the distance between the two building
Form the first equation:
tan θ = opp/adj
tan(30) = x/y
y tan (30) = x
y = x/tan(30)
y = 3x/√3
Form the second equation:
tan θ = opp/adj
tan(60) = (15 + x)/y
y tan(60) = 15 + x
y = (15 + x)/tan(60)
y = (15 + x)/√3
Equate both y:
3x/√3 = (15 + x)/√3
3x = 15 - x
2x = 15
x = 7.5 m
Find y:
y = 3x/√3
y = 3(7.5)/√3
y = 7.5√3 m
Height of the tower = x + 15 = 7.5 + 15 = 22.5 m
Distance between the two building = y = 7.5√3 m
Answer: Height = 22.5 m, Distance = 7.5√3 m
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Step-by-step explanation: