Question

find the length of the missing sides of the triangle. for any answers with a square root, simplify and write your answer in the form sqrt(_) with no spaces.

\\(a = \\)

\\(b = \\)

Explanation:

⚡ Using what you learned: special right triangles (45-45-90 and 30-60-90)

Step 1: Identify the triangle type

The given triangle is a right triangle with an acute angle of \( 45^\circ \). This makes it a \( 45^\circ\text{-}45^\circ\text{-}90^\circ \) special right triangle, which is isosceles.

Step 2: Find side b

In a \( 45^\circ\text{-}45^\circ\text{-}90^\circ \) triangle, the two legs are equal in length.

$$ b = 19 $$

Step 3: Find side a

The hypotenuse \( a \) is equal to the leg length multiplied by \( \sqrt{2} \).

$$ a = 19\sqrt{2} $$

Following the requested formatting for square roots:

$$ a = 19\text{sqrt}(2) $$

Answer:

a = 19sqrt(2)
b = 19