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# In the adjoining figure, not drawn to the scale, AB is a tower and two objects C and D are located on the ground, on the same side of AB. When observed from the top A of the tower, their angles of depression are 45 and 60. Find the distance between the two objects. If the height of the tower is 30. Give your answer to the nearest metre.

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sir this is the important  question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances
AB is a tower and two objects C and D are located on the ground,
on the same side of AB. When observed from the top A of the tower,
their angles of depression are 45 and 60. Find the distance between the two objects.
If the height of the tower is 30.
question no 24 , heights and distances , ICSE board

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1. Consider CB = x and DB = y

AB = 300 m

In right triangle ACD

tan θ = AB/CB

Substituting the values

tan 450 = 300/x

1 = 300/x

So we get

x = 300 m

tan θ = AB/DB

Substituting the values

tan 600 = 300/y

√3 = 300/y

By further calculation

y = 300/√3

Multiply and divide by √3

y = 300/√3 × √3/√3 = 300√3/3

So we get

y = 100 × 1.732 = 173.2 m

Here

CD = x – y = 300 – 173.2 = 126.8 = 127 m

Hence, the distance between two objects is 127 m.

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