Question

write an equation to solve for x
do not solve!
(there is a right triangle with right angle at c, leg bc = 90, leg ac = x, hypotenuse ab = 108)

Explanation:

Step1: Identify the triangle type

The triangle is a right - triangle with right angle at \(C\), so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(a^{2}+b^{2}=c^{2}\).

Step2: Assign values to the sides

Here, one leg is \(x\) (length of \(AC\)), one leg is \(90\) (length of \(BC\)) and the hypotenuse is \(108\) (length of \(AB\)).
Using the Pythagorean theorem, we substitute \(a = x\), \(b=90\) and \(c = 108\) into the formula \(a^{2}+b^{2}=c^{2}\).
We get the equation \(x^{2}+90^{2}=108^{2}\).

Answer:

\(x^{2}+90^{2}=108^{2}\)