Question

A 1.5 meter tall person is standing in front of 41.5
meters high tree. When observing the top of the
tree an angle of 45° is formed with the eyes. Find
the distance between the tree and the person.

Answer 1

Let the boy was standing at point S initially. He walked towards the building and reached at point T.

It can be observed that,

PR=PQ−RQ

⇒ PR=(30−1.5)m=28.5m=

2

57

In △PAR,

AR

PR

=tan30

o

⇒

2AR

57

=

3

1

∴ AR=

2

57

3

m

In △PRB,

BR

PR

=tan60

o

2BR

57

=

3

∴ BR=

2

3

57

=

2

19

3

m

We know, ST=AB

⇒ AB=AR−BR=(

2

57

3

−

2

19

3

)m

∴ AB=

2

38

3

m=19

3

m

solution