Question

Find the value of y. give an exact answer.

Answer 1

y = 8√2

Explanation:

First, we can use the 30-60-90 triangle rule on the rightmost triangle. This states that:

• the hypotenuse is twice the short leg
• the long leg is √3 times the short leg

So, we can solve for the middle line (I will call it L) on this triangle:

L = 16 / 2

L = 8

Next, we can solve for y using the rule with 45-45-90 triangles:

• the legs are congruent
• the hypotenuse is √2 times the length of the legs

So, we can solve for y:

y = 8 · √2

y = 8√2