Question

The height of a tree is √3 times the length of its shadow Find the angle of elevation of the sun

Answer 1

The height of a tree is root(3) ...time the length of the shadow.(given)
so let length of the shadow be h...so height is root(3)*h...
tan(angle)=height/base
tan(angle)=root(3)*h/h
tan(angle)=root(3)
therefore the angle of elevation is 60....since tan 60=root(3)....((also the sun rays are almost perpendicular to the earth...----this is assumpted))

Answer 2

given,
               the height of the tree (h)  AB = √3 and BC = 1
                     let angle c be Ф
                              so angle of elevation taken as tanФ
                                        tanФ = opposite to Ф/adjacent to Ф
                           in ΔABC
                                       tanФ= AB/BC
                                         tanФ=√3/1 = √3
                                  tanФ = √3
             we know that tan 60° = √3
                                so ,
                                            tanФ = √3
                                           tanФ = tan 60°
                                           ∵ Ф = 60°

so,the angle of elevation of the sun is 60°
!hope this helpful!