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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.

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luisejr77

Answer:

[tex]15\sqrt{2}\ ft[/tex] ≈ [tex]21.21\ ft[/tex]

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":

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

For this case:

[tex]\alpha=45\°\\adjacent=15\\ hypotenuse=d[/tex]

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

[tex]cos(45\°)=\frac{15}{d}\\\\d*cos(45\°)=15\\\\d=\frac{15}{cos(45\°)}[/tex]

[tex]d=15\sqrt{2}\ ft[/tex] ≈ [tex]21.21\ ft[/tex]

Ver imagen luisejr77

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