Answer:
[tex]P_1 = 24cm[/tex]
Step-by-step explanation:
Represent:
Phil's height with P
Suzanne's height with S
Phil's shadow with P1
Suzanne's shadow with S1
So, we have:
[tex]P = 51.2cm[/tex]
[tex]S = 5'4"[/tex]
[tex]S_1 = 76.2cm[/tex]
Required
Calculate the length of Phil's shadow --- Missing part of question
To do this, we make use of the following equivalent ratio.
[tex]P:S = P_1 : S_1[/tex]
Convert [tex]S = 5'4"[/tex] to cm
[tex]S = 5ft\ 4in[/tex]
[tex]S = (5*30.48+ 4*2.54)cm[/tex]
[tex]S = 162.56cm[/tex]
Substitute values for P, S and S1
[tex]51.2cm : 162.56cm = P_1 : 76.2cm[/tex]
Express as fraction
[tex]\frac{51.2cm}{162.56cm} = \frac{P_1 }{ 76.2cm}[/tex]
Make P1 the subject
[tex]P_1 = 76.2cm * \frac{51.2cm}{162.56cm}[/tex]
[tex]P_1 = 76.2cm * \frac{51.2}{162.56}[/tex]
[tex]P_1 = \frac{76.2cm * 51.2}{162.56}[/tex]
[tex]P_1 = \frac{3901.44cm}{162.56}[/tex]
[tex]P_1 = 24cm[/tex]
Hence, the length of Phil's shadow is 24 cm
