There is a plane on top of a triangle with angles of 40 degrees and 80 degrees. The 40 degree angle is on the bottom left and the side opposite is Y. The 80 degrees angle is on the bottom right and the side opposite is X.
So... What is X and what is Y?
if all you have is angles, there is no way to find the sides. All similar triangles have the same angles, but different sides.
However, you do know that
X/sin40 = Y/sin80
what's the stuff about a plane on top? What does that have to do with anything?
boring
To find the values of X and Y, we can use the properties of triangles. Specifically, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all sides and angles in the triangle.
Let's consider side Y and angle 40 degrees. According to the Law of Sines, we have the following relationship:
Y / sin(40 degrees) = hypotenuse / sin(80 degrees)
To find X, we can consider side X and angle 80 degrees. Using the Law of Sines:
X / sin(80 degrees) = hypotenuse / sin(40 degrees)
Now, we need to find the value of the hypotenuse. Since the sum of the angles in a triangle is 180 degrees, we can find the third angle by subtracting the sum of the other two angles from 180 degrees:
Third angle = 180 degrees - 40 degrees - 80 degrees = 60 degrees
Now, using the Law of Sines:
hypotenuse / sin(60 degrees) = Y / sin(40 degrees) = X / sin(80 degrees)
Since the hypotenuse is the same in both equations, we can set the two ratios equal to each other:
Y / sin(40 degrees) = X / sin(80 degrees)
Now, we can rearrange this equation to solve for X:
X = Y * sin(80 degrees) / sin(40 degrees)
To find the values of X and Y, you need to know the length of one of the sides (Y or X). Without that information, it's not possible to calculate their exact values.