from the top of a hill the angle of depression of two consecutive kilometre stones due east are found to be 30 degrees ahd 45 degrees respectively. find the distance of the two stones from the foot of the hill.

Asked by pradipdhole | 17th Jun, 2019, 07:39: PM

Expert Answer:

AB is the hill. Point C and D are the positions of the stones on the ground such that CD = 1 km
In ΔABC 
AB/BC = tan 45°
AB/BC = 1
BC = AB ....(i)
In ΔABD 
AB/BD = tan 30°
AB/BD = 1/√3
BD = √3 AB ....(ii)
CD = 1 km
BD - BC = 1 km
√3 AB - AB = 1
(√3 - 1)AB = 1
AB = 1/(√3 - 1)
AB = (√3 + 1)/2 km
Hence, the height of the hill is (√3 + 1)/2 km

Answered by Sneha shidid | 18th Jun, 2019, 09:45: AM