Question

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

Answer 1

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" = $\dfrac{1}{12}$ × 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 = $\dfrac{\textrm perpendicular}{\textrm base}$

Or, Tan Ф = $\dfrac{\textrm AB}{\textrm AO}$

Or, Tan 60° =  $\dfrac{\textrm H}{\textrm X}$

Or, Tan 60° =  $\dfrac{\textrm 5.5 feet}{\textrm X}$

Or, 1.732 = $\dfrac{\textrm 5.5 feet}{\textrm X}$

Or, X = $\dfrac{\textrm 5.5 feet}{\textrm 1.732}$

∴    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