Question

Pleaaaaaaaase
For today

Answer 1

23.6

Explanation:

Hello There!

So they want us to find ∠Z

We are given ∠Zs opposite side length and the length of the hypotenuse

Sine refers to opposite divided by hypotenuse

So we can use sine to solve for ∠Z

`SinZ=(6)/(15) \\(6)/(15) =.4\\SinZ=.4\\Z=arcsin(.4)\\Z=23.57817848`

Note: arcsin is the inverse of sin

Other way we could find ∠Z:

We could also use law of sines which states that a side length divided by sin(its opposite angle) is equal to a different side length divided by sin ( its opposite angle)

So specifically for this triangle

`(15)/(sin90) =(6)/(sinZ)`

step 1 multiply each side by 6

note : flip the fraction

`(6sin90)/(15) =sinZ\\(6sin90)/(15)=.4\\.4=sinZ\\arcin(.4)=23.57817848\\Z=23.57817848`

Then our final step is to give our answer to the first decimal place

so the answer would be 23.6