Question

Use special right triangles to solve for y.

Answer 1

`\sin(45°) = (7)/(y) \Leftrightarrow y = (7)/( \sin(45°)) = (7)/( (1)/( √(2) ) ) = 7 √(2)`

Answer 2

`y=7√(2)`

Explanation:

Notice that the problem is about a right triangle, where the opposite leg is 7 and the acute angle is 45°.

This is an special right triangle because it has acute angles of 45°, that means the legs are congruent, because it's a symmetric right triangle. Basically, when a right triangle has acute angles of 45°, it means is an isosceles triangle too.

Additionally, a special right triangle like this has a pattern, its hypothenuse is
`x√(2)`, where
`x` is the length of a leg.

So, in this case, the hypothenuse is

`y=7√(2)`

And the missing leg is
`x=7`.