Question

Determine the value of y. Use the Pythagorean Theorem and round answer to the nearest tenth. Show your work. Hint: y does NOT equal 8.

Answer 1

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;

`\begin{gathered} c^2=a^2+b^2 \\ \\ Where, \\ \\ c=hypotenuse,\text{ }a,b=other\text{ }sides. \end{gathered}`

We can now substitute values and we'll have;

`\begin{gathered} y^2=3^2+8^2 \\ \\ y^2=9+64 \\ \\ y^2=73 \end{gathered}`

Now we take the square root of both sides;

`\begin{gathered} y=√(73) \\ \\ y=8.54400374532 \\ \\ Rounded\text{ }to\text{ }the\text{ }nearest\text{ }tenth; \\ \\ y=8.5 \end{gathered}`

ANSWER:

`y=8.5`