Answer:
The value of x is approximately 3.5 inches.
Step-by-step explanation:
Given:
Side OC = 5 in
Side DC = 7 in
side OP = x
We need to find the value of x.
Solution:
Now In Δ COD;
m∠COD = 90°⇒(Given in the figure)
So by using Pythagoras theorem we get;
[tex]OD^2+OC^2 = DC^2\\\\OD^2 = DC^2-OC^2[/tex]
Substituting the values we get;
[tex]OD^2= 7^2-5^2\\\\OD^2=49-25\\\\OD^2= 24[/tex]
Now Squaring on both sides we get;
[tex]\sqrt{OD^2} =\sqrt{24} \\\\OD\approx 4.90\ in.[/tex]
Now [tex]Sin\theta= \frac{\textrm{Opposite side}}{\textrm{Hypotenuse}}[/tex]
Sin D = [tex]\frac{Side\ OC}{Side\ DC}[/tex]
So, Sin D = [tex]\frac{5}{7}[/tex] ⇒ equation 1
Now In Δ DPO;
m∠DPO = 90°⇒(Given in the figure)
Also Now [tex]Sin\theta= \frac{\textrm{Opposite side}}{\textrm{Hypotenuse}}[/tex]
Sin D = [tex]\frac{Side\ DP}{Side\ OD}[/tex]
So, Sin D = [tex]\frac{x}{4.9}[/tex] ⇒ equation 2
Hence we can Left hand side of equation 1 and equation 2 are same;
So we can say that Right hand side will be equal too.
Hence equation can be framed as;
[tex]\frac{x}{4.9} = \frac{5}{7}\\\\x = \frac{5}{7} \times 4.9\\\\x\approx 3.5\ in[/tex]
Hence, The value of x is approximately 3.5 inches.
