Question

7.1.ps - 17
find the length of the unknown leg of the right triangle. use pencil and paper. draw the triangle on graph paper and measure to verify the answer.
the length of the unknown leg of the right triangle is
(the figure is not drawn to scale)
22.75
27.25

Explanation:

Step1: Recall Pythagorean Theorem

For a right triangle with legs \(a\), \(b\) and hypotenuse \(c\), the Pythagorean Theorem states \(a^{2}+b^{2}=c^{2}\). Let the unknown leg be \(x\), one leg \(a = 22.75\), hypotenuse \(c=27.25\). So we have \(x^{2}+22.75^{2}=27.25^{2}\).

Step2: Solve for \(x^{2}\)

Rearrange the formula to \(x^{2}=27.25^{2}-22.75^{2}\). Using the difference of squares formula \(a^{2}-b^{2}=(a + b)(a - b)\), where \(a = 27.25\), \(b=22.75\). Then \(x^{2}=(27.25 + 22.75)(27.25-22.75)\).

Step3: Calculate the values

First, \(27.25+22.75 = 50\) and \(27.25 - 22.75=4.5\). Then \(x^{2}=50\times4.5=225\).

Step4: Find \(x\)

Take the square root of both sides: \(x=\sqrt{225}=15\).

Answer:

15