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 ratio of sides in a 45 - 45 - 90 triangle

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 legs are \(11\) (since the non - hypotenuse sides of a 45 - 45 - 90 triangle are equal) and the hypotenuse is \(x\).

Step2: Set up the equation

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

Step3: Calculate the value of \(x\)

We know that \(\sqrt{2}\approx1.414\). So \(x = 11\times1.414=15.554\)

Answer:

\(x\approx15.6\)