2. Jyothi measured the shadow of a flagpole at various times of the day. Which of the following tables show the correct data that are recorded by Jyothi?
Answers
Answer:
Explanation:
Let OA be the vertical pole of height h and OP
1
,OP
2
and OP
3
be the lengths of shadow.
In Δ AOP
1
, we have
tanθ
1
=
OP
1
OA
=
h
h
=1⇒θ
1
=
4
π
In ΔAOP
2
, we have
tanθ
2
=
OP
2
OA
=
2h
h
=
2
1
θ
2
=tan
−1
1/2
Similarly, in ΔAOP
3
, we have
tanθ
3
=1/3
θ
3
=tan
−1
(1/3)
Therefore, sum of the angles of elevation of the eyes
=θ
1
+θ
2
+θ
3
=
4
π
+tan
−1
(
2
1
)+tan
−1
(
3
1
)
=
4
π
+tan
−1
⎝
⎜
⎜
⎛
1−
3
1
×
2
1
2
1
+
3
1
⎠
⎟
⎟
⎞
[∵tan
−1
x+tan
−1
y=tan
−1
(
1−xy
x+y
)]
=
4
π
+tan
−1
(
5/6
5/6
)
=
4
π
+tan
−1
(1)=
4
π
+
4
π
=
2
π