Question

set up and finish: 45 - 45 - 90 #1
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, this would be step 2.
solve your equation above for x.
round to the nearest tenth.

Explanation:

Step1: Recall the property of 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, the ratio of the sides is \(1:1:\sqrt{2}\). If the length of each of the legs is \(a\), and the length of the hypotenuse is \(c\), then \(c = a\sqrt{2}\). Here, \(a = 11\) and \(c=x\).

Step2: Set up the equation

Using the 45 - 45 - 90 triangle ratio, the equation is \(x=11\sqrt{2}\).

Step3: Calculate the value of \(x\)

We know that \(\sqrt{2}\approx1.414\). So \(x = 11\times1.414=15.554\approx15.6\) (rounded to the nearest tenth).

Answer:

The equation is \(x = 11\sqrt{2}\) and \(x\approx15.6\) units.