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

Answer:

$15\sqrt{2}\ ft$ ≈ $21.21\ ft$

Step-by-step explanation:

Observe the figure attached.

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

$cos\alpha=\frac{adjacent}{hypotenuse}$

For this case:

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

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

$cos(45\°)=\frac{15}{d}\\\\d*cos(45\°)=15\\\\d=\frac{15}{cos(45\°)}$

$d=15\sqrt{2}\ ft$ ≈ $21.21\ ft$