Question

Find the x to the nearest tenth using this picture.

Answer 1

21.1

Explanation:

sin 49 = x / 28

0.75470958 = x/28

x = 21.1

Answer 2

x=18.4

y=35

Explanation:

So to solve for x, you're going to use one of the six trigonometric functions (you really only need to use the three main ones, sin, cos, and tan, to solve these problems). In this case you know the adjacent of the angle 49 degrees, and the hypotenuse. There is a trigonometric function which is defined as:
`(adjacent)/(hypotenuse)=cos(\theta)`. So let's plug in the known values:

`cos(49) = (x)/(28)`

Multiply both sides by 28

`cos(49) * 28 = x\\`

Calculate cos(49) using a calculator (make sure it's in degree mode):

`0.656 * 28 \approx x`

`18.4 \approx x`

So the second problem, you need to use the inverse of one of the trigonometric function, which essentially takes what f(x) is, and returns x. So in this case we're looking for a trigonometric function that is defined using the opposite and adjacent side, which tan is.
`tan(\theta)=(opposite)/(adajcent)`. In this case opposite=19, and adjacent=27. So plug in the known values:

`tan(y)=(19)/(27)`

Apply the inverse of tan to both sides

`y=tan^(-1)((19)/(27))`

Calculate inverse of tan of 19/27 using a calculator:

`y\approx35`