The shadow of tower standing on level ground is found to be 45m when sun altitude is 30° than when it was at 60°. Find the height of the tower?
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Answer:
H=39
Step-by-step explanation:
Let h be the height of tower and l be the length of the shadow.
Length of the shadow due to sun at altitude θ is given by -
l = h / tanθ
Shadow at 30° angle will be -
l1 = h / tanθ1
l1 = h / tan30°
Shadow at 60° angle will be -
l2 = h / tanθ2
l2 = h / tan60°
Given that shadow at 30° is longer by 45 m than that at 60° altitude -
l1 - l2 = (h/tan30°) - (h/tan60°)
45 = h (1/tan30° - 1/tan60°)
45 = h (1/0.578 - 1/1.732)
45 = h × 1.153
h = 45 / 1.153
h = 39 m
Therefore, height of the tower would be 39 m.
hope it's helps you....
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