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Question
From two points A and B on the same side of a building, the angles of elevation of the top of the building are 30° and 60° respectively. If the height of the building is 10 m, find the distance between A and B correct to two decimal places.
Solution
Let CD is building A and B are two given points using horizontally on the same side of building.
In Δ DBC,
tan 60° = `"DC"/"CB"`
√3 = `10/y` .....(1)
In Δ DCA,
tan 30° = `"DC"/"CA"`
`1/(√3) = 10/(x + y)` .....(2)
From (1), put y = `10/sqrt3` in (2), we get
`1/sqrt3 = 10/(x + 10/sqrt3)`
`1/sqrt3 = (10sqrt3)/(sqrt3x + 10)`
30 = √3x + 10
x = `20/sqrt3`
x = 11.55 m.
Hence, distance between two points A and B is 11.55 m.
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