. From the top of a hill the angles of depression


of two consecutive kilometer stones due east are found to be30º an45º . Find the height of the hill

A: 1.365 km

B: 1.5 km

C: 1.7 km

D: 1.1 km

 

Best Answer

Explanation:

We will have the figure as,

 depression

Where, AB=h km, is the height of the hill. P,Q are two consecutive kilometer stones.

And BP=x km

In ABP, tan 45=ABBP

1=hx     

x=h.........(1)

In ABQ, tan 30=ABBQ

13=hx+1

Using (1), 13=hh+1

h+1=h3

Substituting 3=1.732

h+1=1.732h

0.732h=1

h=10.732

h1.365km

Final Answer:

The height of the hill is 1.365 km. Hence option A is the correct choice.

 

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