Answer:
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 [tex]tan(30^o)[/tex] is the ratio of the opposite (72-in fence) to the adjacent side [tex]L[/tex] of the triangle (the shadow length):
[tex]tan(30^o) = \dfrac{72 in}{L}[/tex]
since
[tex]tan(30^o) = \dfrac{\sqrt{3} }{3}[/tex]
we have
[tex]\dfrac{\sqrt{3} }{3} = \dfrac{72 in}{L}[/tex]
solving for [tex]L[/tex] we get:
[tex]L = 72\sqrt{3}\\\\\boxed{L = 124.71\: in.}[/tex]
Hence, the length of the shadow to the nearest inch is 125 inches.
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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