Question

With method please

Answer 1

57.8º

Explanation:

According to the law of sines
`(sinA)/(a)` =
`(sinb)/(b)` =
`(sinc)/(c)`.

In this triangle we have two sides with two of their angles.

Let's make 8 cm side a with 38º as its angle, and 11 cm side b with x as its angle.

`(sinx)/(11)` =
`(sin38)/(8)`

Now we multiply both sides by 11 to get rid of the denominator on the left.

sinx =
`(11sin38)/(8)`

To find x, we use inverse sine.

x = sin⁻¹ (11sin38/8)

Plug this into a calculator, and you will get 57.837.

Round this to 57.8º

Hope this helps!