Question

Instructions: Use the ratio of a 45-45-90 triangle to solve for the variables. Leave your answers as radicals in simplest form.

Answer 1

Answer:n

Step-by-step explanationaa:

Answer 2

The answers are:

- For the first triangle:
`\( u = 6 \), \( v = 6√(2) \)`

- For the second triangle:
`\( x = 13√(2) \), \( y = 13 \)`

In both triangles, we'll use the properties of a 45-45-90 triangle. In such a triangle, the sides are in the ratio
`\( 1:1:√(2) \),` meaning the legs are congruent, and the hypotenuse is
`\( √(2) \)`times the length of a leg.

For the first triangle with a leg of 6 units:

- Let the legs be of length a .

- Then the hypotenuse v will be
`\( a√(2) \).`

- Given that one leg a = 6 , the hypotenuse
`\( v = 6√(2) \).`

For the second triangle with a hypotenuse of
`\( 13√(2) \)` units:

- Let the legs be of length y and the hypotenuse be x .

- Using the ratio for a 45-45-90 triangle, we have
`\( x = y√(2) \).`

- Given that the hypotenuse
`\( x = 13√(2) \)`, we can find the leg y by dividing the hypotenuse by
`\( √(2) \), resulting in \( y = (13√(2))/(√(2)) = 13 \).`

So for the first triangle, u = 6 and
`\( v = 6√(2) \)`. For the second triangle,
`\( x = 13√(2) \) and \( y = 13 \).`These are the sides' lengths in radical form in their simplest terms. Since the system has been reset, I'll re-execute the code to provide the necessary mathematical operations to confirm these results.

For the first triangle, the leg is given as 6 units, so the hypotenuse
`\( v \) is \( 6√(2) \).`

For the second triangle, with a hypotenuse given as
`\( 13√(2) \) units, the length of each leg \( y \) is 13 units.`