Question

Please help me with this question

Answer 1

4/5

Explanation:

Look at the picture.

`sine=(opposite)/(hypotenuse)`

We need a hypotenuse length.

Use Pythagorean theorem:

`hypotenuse^2=leg^2+leg^2`

We have

`leg=9,\ leg=12,\ hypotenuse=x`

Substitute:

`x^2=9^2+12^2\\\\x^2=81+144\\\\x^2=225\to x=√(225)\\\\x=15`

For the sine we have:

`opposite=12, hypotenuse=15`

Substitute:

`\sin\alpha=(12)/(15)=(12:3)/(15:3)=(4)/(5)`