Q10 of 25 Page 9

From the top of a hill, the angles of depression of two consecutive kilometer stones due east are found to be 30° and 45°. Find the height of the hill.

To find: The height of hill.


Formula Used:



Explanation:



Let AB is the height of the hill.


The distance between C and D is 1 km.


In triangle ABC,




⇒ AB = BC …. (i)


Again, In triangle ABD,







⇒1.732 AB = AB +1


⇒1.732 AB - AB = 1


⇒AB(1.732-1) = 1


⇒AB × 0.732 = 1



= 1.366


Hence height of the hill 1.366 km


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