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14. From the top of a tall building of height 24 m, the angle of depression of the topof another building is 45° whose height is 10 m. Find the distance between thetwo buildings. |
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Answer» Step-by-step explanation: Let AB and CD be the multi-storied building and the building respectively. Let the height of the multi-storied building be HM and the distance between the TWO building be xm AE=CD=8m [ Given ] BE=AB−AE=(h−8)m and AC=DE=xm [ Given ] Now, in △ACB, ⇒ TAN45 o = AC AB
⇒ 1= x h
∴ x=h ---- ( 1 ) In △BDE, ⇒ tan30 o = ED BE
⇒
1
= x h−8
∴ x= 3
(h−8) ------ ( 2 ) ⇒ h= 3
h−8 3
⇒ 3
h−h=8 3
⇒ h( 3
−1)=8 3
⇒ h= 3
−1 8 3
⇒ h= 3
+1 8 3
× 3
+1 3
+1
⇒ h= 3−1 8 3
( 3
+1)
⇒ h= 2 8 3
( 3
+1)
∴ h=(12+4 3
)m ∴ x=(12+4 3
)m [ From ( 1 ) ] ∴ The height of the multi-storied building and the distance between the two buildings is (12+4 3
)m solution |
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