GIVEN:
We are given a diagram showing a kite with sides and diagonals labeled as shown.
Required;
To determine the value of side length y.
Step-by-step solution;
We shall isolate the part of the kite that includes side length y. This is shown below;
The side length y is the hypotenuse. We shall now solve for y, using the Pythagoras' theorem as follows;
[tex]\begin{gathered} c^2=a^2+b^2 \\ \\ Where, \\ \\ c=hypotenuse,\text{ }a,b=other\text{ }sides. \end{gathered}[/tex]
We can now substitute values and we'll have;
[tex]\begin{gathered} y^2=3^2+8^2 \\ \\ y^2=9+64 \\ \\ y^2=73 \end{gathered}[/tex]
Now we take the square root of both sides;
[tex]\begin{gathered} y=\sqrt{73} \\ \\ y=8.54400374532 \\ \\ Rounded\text{ }to\text{ }the\text{ }nearest\text{ }tenth; \\ \\ y=8.5 \end{gathered}[/tex]
ANSWER:
[tex]y=8.5[/tex]
