Question

Could somebody please explain to me how this works?

Answer 1

Step-by-step explanation:

Right Triangles

The right triangles are those who have an internal angle of 90°. There are certain relations that only stand in right triangles, where the larger side is called the hypotenuse and the other two are the legs. The trigonometric relations in a right triangle are:

`\displaystyle sin\alpha=(y)/(h)`

Where y is the opposite side to the angle
`\alpha` and h is the hypotenuse. We also have

`\displaystyle cos\alpha=(x)/(h)`

In this formula, x is the adjacent side to
`\alpha`. Finally, we have

`\displaystyle tan\alpha=(y)/(x)`

We cannot be sure what is the data and what are the results. We'll assume two given values: The base of the triangle x=6m and the angle adjacent to it
`\alpha=15^o`

The sine, cosine, and tangent of some angles called notable or special angles are widely known. Some of these angles are 0°, 30°, 45°, 60°, 90°.

The triangle of this problem has an angle of 15° which trigonometric functions are not so notable, but with some research we find

`\displaystyle cos15^o=(√(6)+√(2))/(4)`

`\displaystyle tan15^o=2-√(3)`

With these values in mind, we can find the rest of the sides of the triangle. For example, to know the value of the hypotenuse, we set

`\displaystyle tan15^o=(x)/(6m)`

Solving for x

`x=6m\ tan15^o=6(2-√(3))=12-6√(3)`

Similarily

`\displaystyle cos\alpha=(6)/(y)`

Solving for y

`\displaystyle y=(6)/(cos\alpha)`

`\displaystyle y=(6)/((√(6)+√(2))/(4))`

`\displaystyle y=(24)/(√(6)+√(2))`

`\displaystyle y=6(√(6)-√(2))`