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

^{o}and 45^{o}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: Option B

##### Explanation

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

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

= (frac{150}{3})

= 50(sqrt{3})cm

(frac{150}{X x Z}) = tan45^{o} = 1

X + Z = 150

X = 150 – Z

= 150 – 50(sqrt{3})

= 50( (sqrt{3}) – (sqrt{3}))m