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

The length of the shadow is 3.17 feet .

Explanation:

Given as :

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

∴ 12" = 1 '

So, 6" =
`(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 =
`(\textrm perpendicular)/(\textrm base)`

Or, Tan Ф =
`(\textrm AB)/(\textrm AO)`

Or, Tan 60° =
`(\textrm H)/(\textrm X)`

Or, Tan 60° =
`(\textrm 5.5 feet)/(\textrm X)`

Or, 1.732 =
`(\textrm 5.5 feet)/(\textrm X)`

Or, X =
`(\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