Answer: ;
Step-by-step explanation:
You can write two expressions that are in terms of 'x' and 'y'. This is a right triangle, so Pythagorean's theorem can be used. We can also use the angle to find the sine of 30 degrees.
<u>Pythagorean's Theorem:</u>
The values 'a' and 'b' are the two shorter sides of the triangle, while the value 'c' is the longest side of the triangle; the hypotenuse.
<u>Sine of the Angle:</u>
Sine is defined to be the opposite side divided by the hypotenuse. Let's take the sine of 30 degrees:
Plug this value of 'y' into the first expression derived from Pythagorean's theorem:
Use this value of 'x' to solve for 'y' in the expression from Pythagorean's theorem: