A flagstaff stands in the centre of a rectangular field whose diagonal is 120 m. It subtends angles of `15^@` and `45^@` at the midpoints of the sides of the field. The height of the flagstaff is

Options

A. 20m
B. `30sqrt(2+sqrt3)m`
C. `30sqrt(2-sqrt3)m`
D. 40m

Answer

C

Explanation

Let OP be the flagstaff of height 'h' standing at the centre O of the rectengular field ABCD subtending angless `15^@ "and" 45^@` at E and F ,respectivily ,

In triangle POE , OE =`hcot15^@=h(2+sqrt3)`
In triangle POF ,OF = ` hcot45^@`=h
`rArr EF = sqrt (h^2=(2+sqrt3)^2h^2)`
`2hsqrt(2+sqrt3)`
Triangles ACB and FEB are similar .
so, AC =2EF
`rArr 120 = 4hsqrt ((2+sqrt 3))` ,
`rArr h = 30/sqrt(2+sqrt3) = 30sqrt(2-sqrt3)`