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From the top of a vertical mast 150m high., two huts on the same ground level ar...


Question

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

Options

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

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

C) 150 \(\sqrt{3}\)m

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

The correct answer is 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

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Dicussion (1)

  • \(\frac{150}{Z}\) = 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

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