Question

Solve for the missing side lenghts. Leave answer in simplest radical form. USE TRIANGLE THEOREM!

Answer 1

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:

`8\sqrt[]{3}`

Since we now have the common leg as 8√3, the hypotenuse of the the larger triangle will be:

`8\sqrt[]{3}(\sqrt[]{2})\text{ = }8\sqrt[]{6}`

Thus, the missing side lengths are:

ANSWER:

X = 8√6