Question

A. What is the value of x? b. What is the measure of angle B?

Answer 1

Answer:

a. $x=4\sqrt{3}$

b.  $m\angle B =60\°$

Step-by-step explanation:

a. The sides of an Equilateral triangle are all equal.

Then, in this case:

$AB=BC=CA=8$

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:

$CD=BD=\frac{8}{2}=4$

Knowing the length CD, you can find "x" using the Pythagorean Theorem. This is:

$a^2=b^2+c^2$

Where "a" is the hypotenuse and "b" and "c" are the legs.

In this case:

$a=8\\b=x\\c=4$

Substituting values and solving for "x", you get:

$8^2=x^2+4^2\\\\\sqrt{8^2-4^2}=x\\\\x=4\sqrt{3}$

b. By definition, the measure of each interior angle of an Equilateral triangle is 60 degrees. Therefore:

 $m\angle B =60\°$