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ABCD is a rectangle-shaped plot. A lamp post of height 12 m is fixed vertically at corner A. If the angle subtended by the top of the post at B is 60° and at C is 45°, then the area of the plot is

1. 48√2 sq.m
2. 48√3 sq.m
3. 48 sq.m
4. 12√2 sq.m

Correct answer: 48√2 sq.m

Solution

From B the elevation 60 gives AB=12/tan60=4sqrt3; from C the elevation 45 gives the diagonal AC=12. Then the other side AD=sqrt(AC^2-AB^2)=sqrt(144-48)=4sqrt6, so area = AB*AD = 4sqrt3 * 4sqrt6 = 48sqrt2 sq.m.

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