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
150(1 + \(\sqrt{3}\))m
50( \(\sqrt{3}\) - \(\sqrt{3}\))m
150 \(\sqrt{3}\)m
\(\frac{50}{\sqrt{3}}\)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