Question

Abcd is a rectangular field. a vertical lamp post of height 12 m stands at the corner

a. if the angle of elevation of its top from b is 60° and from c is 45° then the area of field is

Answer 1

The area of the field is 48√2 m^2.

Explanation:

Let AE is a vertical lamp post.

AE = h = 12 m

Tan(60°) = 12/AB

AB = 12/√3 = 4√3 m

Tan 45° = 12 / AC =>AC = 12 m

BC = √[(12)^2 - (4√3)^2 ]= √96

=√( 4 × 4 × 3 × 2) = 4√6 m

Area of the field = 4√3 × 4√6

= 16√18 = 16√(3×3×2) = 48√2 m^2 Or 67.88 m^2

Hence the area of the field is 48√2 m^2.

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