Question

19. Small Island in the middle of 100 m wide river and a tall tree stands on the island two pointsP and Q are
directly opposite to each other on the banks and points and trees are in a line suppose the angle of
elevation of the top of the tree from P and Q are respectively 30'and 45°
a) find the height of the tree
take (V3 = 1.732 )
i) 36.6 m
ii) 38.8 m
iii) 39 m
iv) 37 m
b) which point is the farthest from the tree
i) P
ii)
iii) do not say anything iv) not clear
Page No. 2-4
c) find the distance from a point Q to the top of the tree
i) 36.6 m ii) 56.8 m
iii) 51.75 m
iv) 52.3 m
d) If the angle of elevation of the Sun, above a tower increases then the length of shadow of tower
i) increase ii) decrease
iii) increase or decrease iv) none of these
e) The Angles of elevation and depression are always be
i) acute ii) obtuse
iil) right angle
iv) none of these
11 case study
​

Answer 1

Step-by-step explanation:

Let OA be the tree of height h metre.

In triangle POA and QOA, we have

tan 30

∘

=

OP

OA

and tan 45

∘

=

OQ

OA

⇒

3

1

=

OP

h

and1=

OQ

h

⇒OP=

3

handOQ=h

⇒OP+OQ=

3

h+h

⇒PQ=(

3

+1)h

⇒100=(

3

+1)h[∵PQ=100m]

⇒h=

3

+1

100

m

⇒h=

2

100(

3

+1)

m

⇒h=50(1.732−1)m=36.6m

Hence, the height of the tree is 36.6 m.