Question

How do i solve this question?

Answer 1

`x = 18`

`y = 6√(3)`

Explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of a right triangle is called the hypotenuse and the other two sides are called the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides as follows:

Cosine Ratio

`\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}`

Sine Ratio

`\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}`

Consider the angle of θ=30°, then we can write:

`\displaystyle \cos 30^\circ=(x)/(12√(3))`

Solving for x:

`x=12√(3)\cos 30^\circ`

Since:

`\cos 30^\circ=(√(3))/(2)`

Then:

`x=12√(3)\cdot (√(3))/(2)`

`x = 18`

Now apply the sine:

`\displaystyle \sin 30^\circ=(y)/(12√(3))`

Solving for y:

`y=12√(3)\sin 30^\circ`

Since:

`\sin 30^\circ=(1)/(2)`

Then:

`y=12√(3)\cdot (1)/(2)`

`y = 6√(3)`

Answer:

`x = 18`

`y = 6√(3)`