Question

Find the value of x.

Answer 1

Answer:

$4\sqrt{2}$ units

Step-by-step explanation:

In this right triangle the measure of one interior acute angle is 60°, then the measure of second acute angle is

90°-60°=30°.

The leg that is opposite to the angle of 30° is half of the hypotenuse. If x is opposite to the 30° angle, then the hypotenuse is 2x.

By the Pythagorean theorem,

$(4\sqrt{6})^2+x^2=(2x)^2,\\ \\96+x^2=4x^2,\\ \\4x^2-x^2=96,\\ \\3x^2=96,\\ \\x^2=32,\\ \\x=\sqrt{32}=4\sqrt{2}\ units.$