Question

set up and finish: 45 - 45 - 90 #2
write an equation that can be used to solve for the missing side
length. your equation must relate back to the 45 - 45 - 90 special
triangle. from the last slide 3, this would be step 2.
solve your equation above for y.
round to the nearest tenth.

Explanation:

Step1: Recall the 45 - 45 - 90 triangle ratio

In a 45 - 45 - 90 triangle, the ratio of the sides is \(1:1:\sqrt{2}\). Let the legs be of length \(a\) and the hypotenuse be \(c\). Then \(c = a\sqrt{2}\). Here, the hypotenuse \(c=\sqrt{13}\) and the leg \(a = y\). The equation is \(\sqrt{13}=y\sqrt{2}\).

Step2: Solve for \(y\)

Divide both sides of the equation \(\sqrt{13}=y\sqrt{2}\) by \(\sqrt{2}\). We get \(y=\frac{\sqrt{13}}{\sqrt{2}}\). Rationalize the denominator: \(y=\frac{\sqrt{13}\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{\sqrt{26}}{2}\).
Now, calculate \(\sqrt{26}\approx5.1\). Then \(y=\frac{5.1}{2}=2.6\) (rounded to the nearest tenth).

Answer:

The equation is \(\sqrt{13}=y\sqrt{2}\) and \(y = 2.6\) units.