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 60o and 45o 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: B
Explanation
\(\frac{150}{Z}\) = 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
