Question

NEED HELP ASAP PLEASE AND THANK YOU

Answer 1

[1st Picture] Answer: x = 3.98

Explanation:

We are given the opposite side and adjacent side from our reference angle. This will use the tangent function. tanθ =
`(opposite)/(adjacent)`.

tan(53°) =
`(x)/(3)`

3tan(53°) = x

x = 3.98

[2nd Picture] Answer: x = 3.13

Explanation:

Here, we are given the opposite side from our reference angle and the hypotenuse. This will use the sine function. sinθ =
`(opposite)/(hypotenuse)`.

sin(23°) =
`(x)/(8)`

8sin(23°) = x

x = 3.13

[3rd Picture - #6] Answer: θ = 63.4°

Explanation:

Again, we are given the opposite side from our reference angle and the hypotenuse. This will use the sine function. sinθ =
`(opposite)/(hypotenuse)`. To find the angle measurement of theta at the end, we will use the inverse of sine.

sin(θ) =
`(6)/(6.71)`

`sin^(-1)`(sin(θ)) =
`sin^(-1)`(
`(6)/(6.71)`)

θ = 63.4°