Question

check for understanding: 45 - 45 - 90
due on 09.05.2025 not graded
directions
answer the question below to check your understanding and move forward in the course! this quiz is not graded.
find the missing sides of the triangle.
select the correct answer
11
11√2
\frac{11√2}{2}

Explanation:

Step1: Recall 45 - 45 - 90 triangle ratio

In a 45 - 45 - 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$. Let the length of each of the legs be $a$ and the length of the hypotenuse be $c$. Then $c = a\sqrt{2}$.

Step2: Identify given side

The hypotenuse $c = 11$.

Step3: Solve for the legs

Since $c=a\sqrt{2}$, then $a=\frac{c}{\sqrt{2}}$. Rationalizing the denominator, $a = \frac{11}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{11\sqrt{2}}{2}$.

Answer:

$\frac{11\sqrt{2}}{2}$