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 45 - 45 - 90 triangle ratio

In a 45 - 45 - 90 triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the legs are of equal length and the hypotenuse \(c\) is related to a leg \(a\) by \(c = a\sqrt{2}\). Here, the legs are of length \(11\) and the hypotenuse is \(x\).

Step2: Set up the equation

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

Step3: Solve for \(x\)

Calculate \(x = 11\sqrt{2}\approx11\times1.414 = 15.554\approx15.6\)

Answer:

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