Question

Use special right triangles to solve for y.

Answer 1

$\sin(45°) = \frac{7}{y} \Leftrightarrow y = \frac{7}{ \sin(45°)} = \frac{7}{ \frac{1}{ \sqrt{2} } } = 7 \sqrt{2}$

Answer 2

Answer:

$y=7\sqrt{2}$

Step-by-step 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 $x\sqrt{2}$, where $x$ is the length of a leg.

So, in this case, the hypothenuse is

$y=7\sqrt{2}$

And the missing leg is $x=7$.