if the length of the shadow of a tower is increasing then the angle of elevation of the sun also increases is it true?
Answers
Answer: False.
Step-by-step explanation:
Because length of shadow decreases if the angle of elevation of the sun increase.
Answer:
if the elevation moves towards the tower, it increases and if its elevation moves away from the tower, it decreases. Hence, if the shadow of a tower is increasing, then the angle of elevation of the Sun is not increasing.
Step-by-step explanation:
The statement is false.
To understand the fact of this question, consider the following example
I. A tower
2
√
3
m
high casts a shadow 2m long on the ground, then the Sun’s elevation is
60
∘
In
Δ
A
C
B
,
t
a
n
θ
=
A
B
B
C
=
2
√
3
2
⇒
t
a
n
θ
=
√
3
=
t
a
n
60
∘
∴
θ
=
60
∘
II. A same height of tower casts a shadow 4m more from preceding point, then the Sun’s elevation is
30
∘
.
In
Δ
A
P
B
,
t
a
n
θ
=
A
B
P
B
=
A
B
P
C
+
C
B
⇒
t
a
n
θ
=
2
√
3
4
+
2
=
2
√
3
6
⇒
t
a
n
θ
=
√
3
3
.
√
3
3
=
3
3
√
3
⇒=
1
√
3
=
t
a
n
30
∘
∴
θ
=
30
Hence, we conclude from above two examples that if the length of the shadow of a tower is increasing, then the angle of elevation of the Sun is decreasing.
Alternate Method:
We know that, if the elevation moves towards the tower, it increases and if its elevation moves away from the tower, it decreases. Hence, if the shadow of a tower is increasing, then the angle of elevation of the Sun is not increasing.
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