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
jamb 1998mathematics

The correct answer is B. 50( \(\sqrt{3}\) - \(\sqrt{3}\))m

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

,

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

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

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

\(\frac{150}{X x Z}\) = tan45

= 1

X + Z = 150

X = 150 - Z

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

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

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