7.4: Challenge Problems
Hint: #4

Notice that ΔXYZ forms a 30-60-90 triangle.

Now use the 30-60-90 shortcuts to find the
length of the hypotenuse ZX and the long leg
YX.
V
W
Z
60°
2
15°
30°
X
Y

Notice that ΔXYV forms a 45-45-90 triangle.

You should already know the length of YX from
the previous step. Next use the 45-45-90
shortcuts to find the length of the second leg
YV and the hypotenuse VX.
V
45°
W
Z
2
45°
X
Y

Notice that ΔVWZ forms another 30-60-90
triangle.

In order to use the 30-60-90 shortcuts, you
need to know one side of the triangle. That
side would be VZ. It’s length is YV – 2.

V
W
60°
Z
60°
2
Finally, find the length of VW.
X
Y


We’re almost there now. Notice that ΔVWX
forms the 15-75-90 triangle.
You already found the lengths of both VW and
VX. You just have to find the length of WX.
That should be easy since you know the
lengths of WZ and ZX.
V
75°
W
Z
2

Finally, to rewrite the side lengths so that VW
is x, just divide all the sides by the length of
VW. Oh, wait, maybe you’ve already done
that…
Y
15°
X