From the top of a vertical mast 150m high., two huts on the same ground level are observed. One due east and the other due west of the mast. Their angles of depression are 60° and 45° respectively. Find the distance between the huts

A.

150(1 + \(\sqrt{3}\))m

B.

50( \(\sqrt{3}\) - \(\sqrt{3}\))m

C.

150 \(\sqrt{3}\)m

D.

\(\frac{50}{\sqrt{3}}\)m

Correct answer is B

\(\frac{150}{Z}\) = tan 60o,

Z = \(\frac{150}{tan 60^o}\)

= \(\frac{150}{3}\)

= 50\(\sqrt{3}\)cm

\(\frac{150}{X x Z}\) = tan45o = 1

X + Z = 150

X = 150 - Z

= 150 - 50\(\sqrt{3}\)

= 50( \(\sqrt{3}\) - \(\sqrt{3}\))m