Question

Pls help me . full working out needed

Answer 1

`y \approx 27.1\°`

Explanation:

First, we can solve for the length of side AC using the trigonometric ratio tangent.

`\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}`

`\tan(53\°) = (AC)/(14)`

`14\tan(53\°)=AC`

`AC \approx 18.58 \text{ cm}`

Now, we can solve for the measure of angle y using the Law of Sines with the length of AC that we just solved for.

`(\sin(A))/(a) = (\sin(B))/(b)` ... where angle
`A` is opposite side
`a`, and
`B` is opposite
`b`

`(\sin(y))/(18.58) = (\sin(31\°))/(21)`

`\sin(y) = (18.58 \cdot \sin(31\°))/(21)`

`y = \sin^(-1)\left((18.58 \cdot \sin(31\°))/(21)\right)`

`\boxed{y \approx 27.1\°}`