The angles of depression of the top and bottom of a 8m tall building from
the top of a multi storied building are 30° and 45°, respectively. Find the
height of the multi storied building.
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Answers
Step-by-step explanation:
Abdul Kalam, in full Avul Pakir Jainulabdeen Abdul Kalam, (born October 15, 1931, Rameswaram, India—died July 27, 2015, Shillong), Indian scientist and politician who played a leading role in the development of India's missile and nuclear weapons programs. He was president of India from 2002 to 2007.12-Feb-2021
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 °= AB / AC
= 1= x/h
∴ x=h ---- ( 1 )
In △BDE,
⇒ tan30 °= BE / BD
= 1/✓3 = h-8/x
∴ x= ✓ 3 (h−8) ------ ( 2 )
⇒ h=✓3h-8✓3
⇒ h(✓3-1)= 8✓3
⇒ h= (8✓3/✓3+1) *(✓3+1)/(✓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 .
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