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A 5'6" person walking down the street notices his shadow. If the angle of elevation from the tip of the shadow to the sun is 60°, what is the length of the shadow(round to 2 decimal places)?
A) 3.18 feet
B) 3.23 feet
C) 8.66 feet
D) 11.00 feet

Respuesta :

Answer:

The length of the shadow is 3.17 feet .

Step-by-step explanation:

Given as :

The height of the person walking on street = H = 5'6''

∴ 12" = 1 '

So, 6" = [tex]\dfrac{1}{12}[/tex] × 6 = 0.5'

I.e H = 5.5 feet

The angle of elevation of from tip of shadow to sun = Ф = 60°

Let The length of the shadow = X feet

Now, From figure'

Tan angle = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]

Or, Tan Ф = [tex]\dfrac{\textrm AB}{\textrm AO}[/tex]

Or, Tan 60° =  [tex]\dfrac{\textrm H}{\textrm X}[/tex]

Or, Tan 60° =  [tex]\dfrac{\textrm 5.5 feet}{\textrm X}[/tex]

Or, 1.732 = [tex]\dfrac{\textrm 5.5 feet}{\textrm X}[/tex]

Or, X = [tex]\dfrac{\textrm 5.5 feet}{\textrm 1.732}[/tex]

∴    X = 3.17 feet

So, The length of the shadow = X = 3.17 feet

Hence, The length of the shadow is 3.17 feet . Answer

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