Use the figure below to find the answer.Use special right triangles to solve for y.

Hello!

The image above displays a right triangle, meaning one of its angles is 90 degrees. We are also given a second angle, whose measure is 45 degrees. We know that the sum of all angles in a triangle will equal 180 degrees. This can be expressed by the following formula:

(angle 1) + (angle 2) + (angle 3) = 180

Using this formula, we can find the value of the third angle. Begin by inserting any known values into the equation above:

90 + 45 + (angle 3) = 180

Simplify the left side:

135 + (angle 3) = 180

Subtract 135 from both sides of the equation:

angle 3 = 45

We have proven the third angle to equal 45 degrees. Because the angles of this triangle are 90, 45, and 45 degrees, this particular triangle can be classified as a "right isosceles triangle." Isosceles simply means that it will have two identical angles (in this case, 45 and 45) and two sides of identical length (in this case, "x" and 7). Because we have proven that "x" and 7 are the same length, we can conclude that "x" is equal to 7.

Now, because this is a right triangle, we can use the Pythagorean Theorem to calculate the value of "y." This theorem states the following:

c² = a² + b²

In this case, A and B are the legs while C represents the hypotenuse (y). Insert any known values into the equation above and simplify:

c² = 7² + 7²
c² = 49 + 49
c² = 98

Now take the square root of both sides:

c = [tex] \sqrt{98} [/tex]
c = 7[tex] \sqrt{2} [/tex]

We have now proven that the value of "y" is 7[tex] \sqrt{2} [/tex]

I hope this helps!