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.
save 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 \(x\) and the hypotenuse be \(h\). Then \(h = x\sqrt{2}\). Here, assume the side length \(y\) is one of the legs of the 45 - 45 - 90 triangle formed (after considering the properties of the square - like figure). The hypotenuse of the 45 - 45 - 90 triangle is \(\sqrt{13}\). So the equation is \(\sqrt{13}=y\sqrt{2}\)

Step2: Solve the equation for \(y\)

From \(\sqrt{13}=y\sqrt{2}\), we can solve for \(y\) by dividing both sides of the equation by \(\sqrt{2}\). So \(y=\frac{\sqrt{13}}{\sqrt{2}}\). Rationalize the denominator: \(y = \frac{\sqrt{13}\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{\sqrt{26}}{2}\)

Step3: Calculate the numerical value

We know that \(\sqrt{26}\approx5.1\), then \(y=\frac{5.1}{2}=2.6\) (rounded to the nearest tenth)

Answer:

\(y = 2.6\)