Question

the angle of elevation of a tree at a place 90 meter away is 15° degree . what is height of tree

Answer 1

So let the height of the tree ( Opposite side ) be ' x '

Distance between the tree and the observer ( Adjacent side ) = 90 meters

Angle of elevation = 15°

So we know that Tan Ф gives us the ratio of measure of opposite and adjacent sides.

=> Tan 15 = Opposite side ( x ) / 90

tan(15) = tan (45 − 30 )= tan (45) − tan (30) / 1 + tan (45) tan (30)

=> Tan 15 = 1 - ( 1 / √3 ) / 1 + ( 1 / √3 )

=> Tan 15 = 2 - √ 3

=> 2 - √3 = x / 90

=> x = 90 ( 2 - √ 3 )

=> x = 180 - 90√3 meters

=> x = 180 - 155.88 = 24.12

Hence the height of the tree is 24.12 meters.

Hope it helped !

Answer 2

Answer:

15

S

x=b÷

=90÷15

10m