From a point on the ground, the angles of elevation of the bottom and top of a water tank kept on the top
of the 30m high building are 30° and 45° respectively. Find the height of the water tank
Answers
If a tank is kept at the top of a building of height 30 m and the angle of elevation of bottom & top of tank is 30° & 45° then the height of the water tank is 30(√3-1) m or 21.96 m.
Step-by-step explanation:
The height of building = 30 m
The angle of elevation from the ground to the bottom of the tank = 30°
The angle of elevation from the ground to the top of the tank = 45°
Let the height of tank CD be “h” m and the distance AB be “x” m(as shown in the figure)
Considering ∆ ADB, we get
tan θ = perpendicular/base = AD/AB
⇒ tan 30 = 30/x ….. [here θ= 30°]
⇒ 1/√3 = 30/x
⇒ x = AB = 30√3 m …… (i)
Now, considering ∆ ABC,
tan θ = AC/AB
⇒ tan 45 = (h+30)/x ….. [here θ= 45°]
⇒ 1 = (h+30)/30√3 …… [substituting the value of x from (i)]
⇒ h = 30√3 – 30
⇒ h = 30[√3 - 1] m or 21.96 m ….. [√3 = 1.732]
Thus, the height of the tank is 30[√3 - 1] m or 21.96 m .
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Step-by-step explanation:
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