Question

4. What are the values of the variables in the triangle below? If your answer is not an integer, leave
it in simplest radical form. The diagram is not drawn to scale.
Ox = 18 3: y = 6
Ox = 18; y = 6.13
Ox= 6; y = 183
Ox= 6.13: y = 18

Answer 1

Using relations in a right triangle, it is found that the values of the variables in the triangle below are given by:

$x = 18, y = 6\sqrt{3}$

What are the relations in a right triangle?

The relations in a right triangle are given as follows:

• The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.

• The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.

• The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this problem, the hypotenuse is of $12\sqrt{3}$, while the opposite angle to side y is of 30º, hence:

$\sin{30^\circ} = \frac{y}{12\sqrt{3}}$

$\frac{1}{2} = \frac{y}{12\sqrt{3}}$

$y = 6\sqrt{3}$

The adjacent side to the angle of 30º is of x, hence:

$\cos{30^\circ} = \frac{x}{12\sqrt{3}}$

$\frac{\sqrt{3}}{2} = \frac{x}{12\sqrt{3}}$

$2x = 36$

$x = 18$

More can be learned about relations in a right triangle at https://brainly.com/question/26396675