A tower is 50 m high. Its shadow is x metres shorter when
the sun's altitude is 45° than when it is 30°. Find the value of x.
[Given V3 = 1.732.]
Answers
Answer:
3660 cm is the value of x, which means the shadow is 3660 cm shorter.
Given:
The tower height = 50 m
Sun’s altitude is 45°when it is 30°.
To find:
Find the value of x which means the shadow shorter to the nearest cm = ?
Solution:
The height of the tower is 50 m high
The length of the shadow is X, when the shadow is being casted at an angle of 45 degrees
When the length of the shadow is being casted at 30 degrees the length of the shadow is X + 50
Therefore, the value of X is
\begin{lgathered}\begin{array}{l}{\tan 45^{\circ}=\frac{A}{l e n g t h \text { of the shadow at } 45}} \\ {\tan 45^{\circ}=\frac{A}{50}} \\ {A=50}\end{array}\end{lgathered}
tan45
∘
=
length of the shadow at 45
A
tan45
∘
=
50
A
A=50
The length of the shadow is X, when the shadow is being casted at an angle of 45 degrees is 50 m
Hence, the length of the tower to the length of the shadow falls at 30 degree is
\begin{lgathered}\begin{array}{l}{\tan 30^{\circ}=\frac{50}{l e n g t h \text { of the shadow at } 30}} \\ {\frac{1}{\sqrt{3}}=\frac{50}{x+50}} \\ {x=50(\sqrt{3}-1)}\end{array}\end{lgathered}
tan30
∘
=
length of the shadow at 30
50
3
1
=
x+50
50
x=50(
3
−1)
Therefore, the value of the X is
\begin{lgathered}\bold{\begin{aligned} 50(\sqrt{3}-1) &=50 \times 0.732 | \\ &=36.6 m \\ &=3660 \mathrm{cm} \end{aligned}}\end{lgathered}
50(
3
−1)
=50×0.732∣
=36.6m
=3660cm