PROBLEM:
In [tex] \tt \triangle ABC[/tex], [tex] \tt AC = 6 cm[/tex], [tex] \tt BC = 8 cm[/tex] and [tex] \tt\angle C = 90°[/tex]. Calculate the length of AB.
SOLUTION:
• To solve for the value of the unknown side in a right triangle, we will use the Pythagorean Theorem which tells us that the area of the square of the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
• The value of c is for the hypotenuse while we'll let a be 8 cm and b for 6 cm.
[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: }}[/tex]
[tex] \large \begin{array}{l} \tt c {}^{2} = a {}^{2} + b {}^{2} \\ \tt c {}^{2} = (8 \: cm) {}^{2} + (6 \: cm) {}^{2} \\ \tt c {}^{2} = 64 \: cm {}^{2} + 36 \: cm {}^{2} \\ \tt c {}^{2} = 1 00 \: cm {}^{2} \\ \tt \sqrt{c {}^{2} } = \sqrt{100 \: cm {}^{2} } \\ \tt c = 10 \: cm\end{array}[/tex]
[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: }}[/tex]
• The square root of 100 results to a positive and negative integer of 10 but since we're talking about lengths, we will disregard the negative one.
ANSWER:
The length of AB is 10 centimeters.
