Question

20.The horizontal distance between two trees of different heights is 60m.If the
angle of elevation of the top of the first tree when seen from the bottom of
second tree is 30°, Find the height of the first tree. If the height of second tree
is 60v3m, then find the angle of elevation of the top of second tree when seen
from the bottom of first tree.
nnnint on the ground 40 m away from the foot of a tower, the angle
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Answer 1

angle made from bottom of 2nd tree to top of first tree 30°

distance between the trees is 60m

height of 1st tree

tan30°=opposite side/adjacent side

$\frac{1}{ \sqrt{3} } = \frac{x}{60} \\ \sqrt{3} x = 60 \\ x = \frac{60}{ \sqrt{3} } \\ \frac{60}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3}} = 20 \sqrt{3}$

height of 2nd tree

$height \: of \: second \: tree \: = 60 \sqrt{3} \\ \tan( \alpha ) = \frac{60 \sqrt{3} }{60} \\ \tan( \alpha ) = \sqrt{3} \\ \tan(60) = \sqrt{3} \\ therefore \: angle \: is \: 60$

angle is 60°