Question

A vertical pole Casts a shadow 21 m long when the altitude of sun is 30 degree.
a) find the height of the pole
b) find the length of Shadow when the altitude of sun is 60 degree.
c) the altitude of Sun when the length of the shadow is 7√3 m.

Answer 1

Answer:

1) 7√3 meters

2) 7 meters

3) 45°

Step-by-step explanation:

A vertical pole Casts a shadow 21 m long when the altitude of sun is 30 degree.

a) To find the height of the pole, apply trigonometric identity

Height of pole = AB

$\tan(30°) = \frac{AB}{AC} \\ \\ \frac{1}{ \sqrt{3} } = \frac{AB}{21} \\ \\ AB= \frac{21}{ \sqrt{3} } \\ \\ AB = 7 \sqrt{3} \: m$

Height of pole= 7√3 m

b) find the length of Shadow when the altitude of sun is 60 degree.

Height of pole = 7√3 m

sun altitude = 60°

$\tan(60°) = \frac{AB}{AC} \\ \\ \sqrt{3} = \frac{7 \sqrt{3} }{AC} \\ \\ AC = \frac{7 \sqrt{3} }{ \sqrt{3} } \\ \\ AC = 7 \: m$

length of Shadow= 7 m

c) the altitude of Sun when the length of the shadow is 7√3 m.

Height of pole AB= 7√3 m

length of shadow AC= 7√3 m

$\tan( \theta) = \frac{AB}{AC} \\ \\ = \frac{7 \sqrt{3} }{7 \sqrt{3} } \\ \\ \tan( \theta) = 1 \\ \\ \tan( \theta) = \tan( 45°) \\ \\ \theta = 45°$

Hope it helps you.

Answer 2

Answer:

√3 meters

2) 7 meters

3) 45°

Step-by-step explanation:

A vertical pole Casts a shadow 21 m long when the altitude of sun is 30 degree.

a) To find the height of the pole, apply trigonometric identity

Height of pole = AB

Height of pole= 7√3 m

b) find the length of Shadow when the altitude of sun is 60 degree.

Height of pole = 7√3 m

sun altitude = 60°

length of Shadow= 7 m

c) the altitude of Sun when the length of the shadow is 7√3 m.

Height of pole AB= 7√3 m

length of shadow AC= 7√3 m

Hope it helps you.

Step-by-step explanation: