Question

Use the diagram of point O. What is the length of OY to the nearest 10th of an Inch? XZ = 10 and OX= 10

Answer 1

From the diagram above,

XZ = 10 in and OX = 10 in

we are to find length of OY

XZ is a chord and line OY divides the chord into equal length

Hence, ZY=YX= 5 in

Now we solve the traingle OXY

To find OY we solve using pythagoras theorem

$(Hyp)^2=(Opp)^2+(Adj)^2$

applying values from the triangle above

$\begin{gathered} OX^2=XY^2+OY^2 \\ 10^2=5^2+OY^2 \\ 100=25+OY^2 \\ OY^2\text{ = 100 -25} \\ OY^2\text{ = 75} \\ OY\text{ = }\sqrt[]{75} \\ OY\text{ = }\sqrt[]{25\text{ }\times\text{ 3}} \\ OY\text{ = 5}\sqrt[]{3\text{ }}in \end{gathered}$

Therefore,

Length of OY =

$5\sqrt[]{3}$