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.

the answer is 21%.