a man on the bank of a stream observes a tree on the opposite bank exactly across the stream he finds the angle of elevation of the top of the tree to be 45. on receding perpendicularly a distance of 4m from the bank, he finds that the angle of elevation reduces by 15 .is this information sufficient for the man to determine the height of the tree and the width of the stream? if so, find them.

   heights and distance

Asked by triptisrivastava2002 | 14th Oct, 2018, 03:26: PM

Expert Answer:

AD is the tree
B is the initial position of man
C is the final position
CB = 4m ......given
we can find the value of AD using given info
apply tan in  tri BAD
you get BA = DA...........eqn.1
then apply tan in CAD
tan 30 = DA/CA
replace CA =  CB + BA, which is CB + DA........from eqn.1
sub value of tan 30 and value of CB
so
1/√3 = DA/(4 + DA).......find DA

Answered by Arun | 19th Oct, 2018, 10:55: AM