Question

From the top of a hill, the angles of elevation of 2 consecutive kilometres stone, due east are formed to be 30° and 45° respectively. Find the distance of the 2 stones from the foot of the hill.

Answer 1

Draw a diagram like in the pic.
Tan 45° =1
therefore AB/BC = 1
therefore AB= BC
now, Tan 30°= 1/√3
1/√3= AB/BC +CD
1/√3= AB/AB + 1 ( distance between stones is 1km)
therefore AB= 1.366 ( by solving the equation... you may have to rationalize the denominator to get the answer)
since AB = 1.366
BC = 1.366 therefore distance from the base to first stone is 1.366km and to the second stone is 2.366km.....
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