Find sin0 where 0 is the angle shown. Give an exact value, not a decimal approximation.

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

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