Answer:
a. [tex]x=4\sqrt{3}[/tex]
b. [tex]m\angle B =60\°[/tex]
Step-by-step explanation:
a. The sides of an Equilateral triangle are all equal.
Then, in this case:
[tex]AB=BC=CA=8[/tex]
Based on this, you can identify that AD divides the side BC into two equal parts and the triangle into two equal Right triangles. Then:
[tex]CD=BD=\frac{8}{2}=4[/tex]
Knowing the length CD, you can find "x" using the Pythagorean Theorem. This is:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs.
In this case:
[tex]a=8\\b=x\\c=4[/tex]
Substituting values and solving for "x", you get:
[tex]8^2=x^2+4^2\\\\\sqrt{8^2-4^2}=x\\\\x=4\sqrt{3}[/tex]
b. By definition, the measure of each interior angle of an Equilateral triangle is 60 degrees. Therefore:
[tex]m\angle B =60\°[/tex]
