Question

Find the exact value of y.

(Please refer to the attachment below)

Answer 1

`√(3)`

Explanation:

Special right triangles help us find the exact values of different side lengths.

Special Right Triangles

Special right triangles are right triangles with specific angles and side proportions. We know that this is a 45-45-90 triangle because the 3 angles are 45, 45, and 90 degrees. Remember that in a right triangle, the shorter side lengths are called the legs and the longest side is the hypotenuse. If the legs are y, then the hypotenuse is y√2. This means that the hypotenuse is √2 times longer than the legs.

Finding y

To solve for y, we can set up an equation.

• 
  `y*√(2) =√(6)`

In order to find the exact value, divide both sides by √2.

• 
  `y=(√(6) )/(√(2) )`

We can further simplify this by dividing the values under the radical.

• 
  `y=√(3)`

For this triangle, y = √3.