Question

From the top of a hill the angle of depression of two consecutive kilometre stones due east are found to be 30 degree and 45 degree. find the height of the hill

Answer 1

▶ Answer :

Height of the Hill is 1.36 km.

▶ Step - By - Step Explanation :

Let AB is the height of the hill and two stones are C and D respectively where depression is 45° and 30° ,

▶ Given : Distance Between C and D = 1 km

Now, In right angled ∆ABC

tan 45° = AB / BC

1 = AB/ BC

•°• BC = AB. -------(A)

Again , In right angled ∆ABD

tan 30 ° = AB / BC + CD



=> 1/√3 = AB / AB+ CD [ •°• AB = BC ]

=> 1/√3 = AB/ AB + 1

=> 1/ 1.732 = AB / AB + 1

=> 1.732AB = AB + 1

=> 1.732AB - AB = 1

=> 0.732AB = 1

=> AB = 1/0.732

=> AB = 1.36 Metres

Hence , Required Height of the Hill is 1.36 km