Answer: w=4, y=4
Step-by-step explanation:
For this problem, we can use the 30-60-90 triangle to find out what the length of w and y are. 30-60-90 triangle is a special triangle. The hypotenuse is 2x in length. It is directly opposite the right angle. The leg opposite of 60° is x√3 in length. The leg opposite of 30° is x. For all 3 legs, wherever you see x, you plug in the same number.
We can look at the figure as 2 separate triangles.
For the triangle on the right, we can see the hypotenuse is 8. Since we know the length of the hypotenuse is 2x, we can plug in 8 for 2x to find x.
2x=8
x=4
Now that we know x=4, we can directly plug it into the lengths above.
W is across from 30°. Above, we have established that the leg across from 30° has the length of x. Since x=4, w=4.
Since w=4, we can use this information to find the length of y by looking on the left triangle. Now, y is across from 30°. In the first paragraph, we stated that the leg across from 30° is x. Since we know x, we can directly plug it into this. After we plug it in, y=4.
