Question

The game is played on a square court divided into four smaller squares that meet at the center. If a line is drawn diagonally from one corner to another​ corner, then a right triangle QTS is​ formed, where angleQTS is 45degrees. Using a trigonometric​ function, find the length of the diagonal for a 15​-foot square court.

Answer 1

`15√(2)\ ft` ≈
`21.21\ ft`

Explanation:

Observe the figure attached.

You need to use the following Trigonometric function in order to find the length of the diagonal "d":

`cos\alpha=(adjacent)/(hypotenuse)`

For this case:

`\alpha=45\°\\adjacent=15\\ hypotenuse=d`

Therefore, you need to substitute these values into the Trigonometric function and solve for "d":

`cos(45\°)=(15)/(d)\\\\d*cos(45\°)=15\\\\d=(15)/(cos(45\°))`

`d=15√(2)\ ft` ≈
`21.21\ ft`