The sun shines at a 30° angle to the ground. To the nearest inch, how long is the shadow cast by a 72-inch tall fence post?

The length of the shadow cast by a 72-inch tall fence post is 144 inches

The set up will form a right triangle

If the sun shines at a 30° angle to the ground by a 72-inch tall fence post, then;

The length of the post = 72 inches

Angle of elevation = 30 degrees

Required side

Length of the shadow (hypotenuse)

Using the SOH CAH TOA identity:

Sin theta = opp/hyp

Sin 30 = 72/l

l = 72/sin30

l = 72/0.5

l = 144 in

Hence the length of the shadow cast by a 72-inch tall fence post is 144 inches

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The shadow length is 125 inches.

Step-by-step explanation:

The triangle that the sun's rays and the fence post form is shown in the figure.

From trigonometry we know that is the ratio of the opposite (72-in fence) to the adjacent side of the triangle (the shadow length):

since

we have

solving for we get:

Hence, the length of the shadow to the nearest inch is 125 inches.

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this