Question

liam is making plans for a garden in the shape of a right triangle. the first side is the longest side and is 19 feet long. if the second side of the garden measures 11 feet and makes a right angle with the third side, how long is the third side, in feet? round your answer to two decimal places. show your work here hint: to add the square root symbol (√), type
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Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side). Let \(c = 19\) (hypotenuse), \(a=11\), and \(b\) be the unknown side. Then \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(c = 19\) and \(a = 11\) into the formula: \(b^{2}=19^{2}-11^{2}\).

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Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{240}\).

$$b=\sqrt{16\times15}=4\sqrt{15}\approx 15.49$$

Answer:

\(15.49\)