Answer:
x = 4√2
Explanation:
Identifying the triangle in the diagram:
- Whenever you see a right angle (its measure is 90°) and a 45°, the measure of the third angle is also 45° and the triangle is called a 45-45-90 triangle which has special rules, as it relates to the lengths of its sides.
45-45-90 triangle rules:
- The two sides across from the 45° are congruent and their lengths are x units long.
- The hypotenuse (always across from the right angle) is the longest side and its length is x√2 units long.
Finding x:
Since the hypotenuse is 8 units long and, we can find x by setting 8 equal to x√2:
(8 = x√2) / √2
8/√2 = x
Rationalize the denominator to simplify:
- When you have a fraction with a root as the denominator, we simplify (i.e. rationalize the denominator) by multiplying both the numerator and denominator by the root, which clears the root on the denominator:
(8/√2) * (√2/√2)
8√2 / 2
4√2
Thus, x = 4√2