Question

the top of a tree is broken by the wind struck the ground at a distance of 100 m from the foot of the tree find the total height of the tree that the angle at which the top struck the ground is (1)60 degree and (2)is 45 degree​

Answer 1

Answer:

a) 216.5 metre

b) 170.7 metre

Step-by-step explanation:

a) therefore

$\sin(60) = \frac{length \: of \: tree \: broken}{length \: of \: tree \: still \: attached} = \frac{ \sqrt{3} }{4}$

$\tan(60) = \frac{length \: of \: tree \: still \: attached \: o \: the \: ground}{distance \: of \: tip \: from \: the \: base \: of \: tree \: on \: ground} = \frac{ \sqrt{3} }{1}$

so, height

of tree still attached =

√3 x 100

=173.2 m

length of tree broken=

=173.2/4

=43.3 m

so, total length of tree =

173.2+43.3

=216.5 metre

b) therefore

$\sin(45) = \frac{length \: of \: broken \: part \: of \: tree}{height \: of \: tree \: still \: attached} = \frac{1}{ \sqrt{2} }$

$\tan(45) = \frac{height \: of \: tree \: still \: attached}{distance \: of \: tip \: from \: base \: on \: the \: ground} = \frac{1}{1}$

so, height of tree still attached =

1 x distance on ground

=100 m

so, length of broken tree

=100/√2

=50√2

*1

so, total length of tree

=100+50√2

=50(2+√2)

=50(2+1.414)

=5 x 34.14

=170.70 metre

Hope this helps you.

Answer 2

Answer :

1. Height of the tree that the angle of 60 deg will be 173.2 m

Distance = 100 m

Height = ? = h

tan 60 = h/100

√3 = h / 100

h = 100 √3

h = 100x1.732

h = 173.2 m

2. Height of the tree that the angle of 45 deg will be 100 m

Distance = 100 m

Height = ? = h

tan 45 = h/100

1 = h / 100

h = 100 m

I hope the above helps