Answer: Sin0 = 8/8.5
Step-by-step explanation: What we have is a right angled triangle, with two sides given and one angle which is the reference angle (unknown angle).
The Sine of the angle is calculated as
Sin0 = opposite/hypotenuse
We have the opposite side (facing the reference angle) as 8 units and the hypotenuse (facing the right angle unknown), which we shall label as X.
To calculate the hypotenuse, we shall apply the Pythagoras theorem which is,
X² = 3² + 8²
X² = 9 + 64
X² = 73
Adding the square root sign to both sides of the equation, we now have
X = √73
X = 8.5 (approximately)
Now that we have the hypotenuse as 8.5, the Sine of the angle can now be calculated as
Sin0 = opposite/hypotenuse
Sin0 = 8/8.5