Afence post is sticking out of the ground tilted at an angle of 70 degrees from horizontal. the length of the post sticking out is 2 meters. when the sun is directly overhead, what is the length of the shadow cast by the post? answer in meters with at least 1% accuracy.
answer

2.584 metres

Explanation:

The angle of elevation made by the pole to the ground is 70.

The height of the pole is 2 metres.

Since sun is directly overhead, the sunlight will make an 90° angle with the pole and cast the shadow.

Hence a triangle will be formed with pole as perpendicular, sunlight as base and shadow as hypotenuse.

Let the shadow be x.

So,

sin 70 = length of pole / x

x = 2 metres / sin 70°

1m

Explanation:

The tilted post forms 70° with the ground

The post length sticking out is 2 meters

The shadow formed will be that cast on the ground for the post.

Applying the formula for finding cosine of an angle, the angle will be 70°, the length of tilted post will form the hypotenuse and while the sun strikes at 90° it forms the shadow of the post as the adjacent length to the angle formed by the tilted post.

Cosine of Ф ° = adjacent length/hypotenuse

Cosine 70°= x/2

0.34202014332=x/2

x=0.34202014332*2= 0.6840 m

At least 1% accuracy means the value should be ±1

So 0.6840 ⇒ 1 m

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