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(3 + \(\sqrt{3}\))m
C
150 \(\sqrt{3}\)m
D
\(\frac{50}{\sqrt{3}}\)m
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Tan60º = \(\frac{150}{y}\)
\(\sqrt{3}\) = \(\frac{150}{y}\)
y = \(\frac{150\sqrt3}{3}\)
y = 50\(\sqrt3\)
Tan45º = \(\frac{150}{z}\)
1 = \(\frac{150}{z}\)
z = 150
But x = z + y
x = 150 + 50\(\sqrt3\)
x = 50(3 +\(\sqrt{3}\))m
Source: Myschool Past Questions Archive (Record #30734)