Answer:
Step-by-step explanation:
The first triangle is a 30-60-90 right triangle. We have a Pythagorean triple associated with this type of triangle that is
(x , x√3, 2x) which represent the side lengths across from the
(30°, 60°, 90°)
We have the side length across from the 30° as 14. That means that x = 14. In our figure, "y" is across from the 60° which means that the side length is
14√3, which has a decimal equivalency of 24.24871131; in our figure "x" is the hypotenuse which is 14(2) which is 28.
For the intents and purposes of keeping you not confused:
x = 28, y = 14√3 (or 24.24871131)
The next triangle is also a right triangle but this one is a 45-45-90. The Pythagorean triple for that triangle is
( x , x , x√2 ) as the side lengths across from the
(45°, 45°, 90°)
We have a side length across from the 90° as 18 units long; therefore, according to our Pythagorean triple:
x√2 = 18 and
x = [tex]\frac{18}{\sqrt{2} }[/tex] and, rationalizing the denominator:
[tex]x=\frac{18\sqrt{2} }{2}[/tex] so
x = 9√2, which has a decimal equivalency of 12.72792206.
Summing up again:
x = 9√2 (or 12.72792206)
