Question

Please help me with this question

Answer 1

Answer:

4/5

Step-by-step explanation:

Look at the picture.

$sine=\dfrac{opposite}{hypotenuse}$

We need a hypotenuse length.

Use Pythagorean theorem:

$hypotenuse^2=leg^2+leg^2$

We have

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

Substitute:

$x^2=9^2+12^2\\\\x^2=81+144\\\\x^2=225\to x=\sqrt{225}\\\\x=15$

For the sine we have:

$opposite=12, hypotenuse=15$

Substitute:

$\sin\alpha=\dfrac{12}{15}=\dfrac{12:3}{15:3}=\dfrac{4}{5}$