The longest side of a right-angled triangle which is opposite to the right angle.
Identify the hypotenuse for the following diagram.
\(AC\) is the side opposite to the right angle.
Thus, \(AC\) is the hypotenuse.
State the relationship between the lengths of sides of the following right-angled triangle.
The relationship is
\(LN^2=LM^2+MN^2\).
Given the following diagram, calculate the value of \(x\).
Give the answer in two decimal places.
\(\begin{aligned} x^2&=9^2+14^2 \\\\&=81+196 \\\\&=277 \\\\x&=\sqrt{277} \\\\&=16.64\text{ cm}. \end{aligned}\)
Calculate the length of \(QS\) in the following diagram.
First, calculate the length of \(QR\).
\(\begin{aligned} QR^2&=PQ^2-PR^2 \\\\&=15^2-12^2 \\\\&=225-144 \\\\&=81 \\\\QR&=\sqrt{81} \\\\&=9\text{ cm}. \end{aligned}\)
Next, calculate the length of \(RS\).
\(\begin{aligned} RS^2&=PS^2-PR^2 \\\\&=13^2-12^2 \\\\&=169-144 \\\\&=25 \\\\RS&=\sqrt{25} \\\\&=5\text{ cm}. \end{aligned}\)
Thus, the length of \(QS\) is
\(\begin{aligned} QS&=QR+RS \\\\&=9+5 \\\\&=14\text{ cm}. \end{aligned}\)
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