We can see that the triangle is a right triangle.
The smaller triangle is a 30-60-90 right triangle
The larger triangle is a 45-45-90 right triangle.
Using the 45-45-90 Triangle Theorem which states that the hypotenus is √2 times the length of a leg and the legs are congruent.
Also we are to use the 30-60-90 triangle theorem which staes that the hypotenuse is 2 times the shorter leg.
Here, the shorter leg is = 8
Thus, the hypotenuse is = 8 x 2 = 16
Also the longer leg is √3 times the shorter leg.
Thus, the longer leg which is the common leg of both triangles is:
[tex]8\sqrt[]{3}[/tex]
Since we now have the common leg as 8√3, the hypotenuse of the the larger triangle will be:
[tex]8\sqrt[]{3}(\sqrt[]{2})\text{ = }8\sqrt[]{6}[/tex]
Thus, the missing side lengths are:
ANSWER:
X = 8√6
