To determine the length of line segment AC using the equation sin(40), we can apply the basic principles of trigonometry. Here’s how it works:
1. **Understanding the Context**: First, we need to understand that the sin function relates the angle to the ratios of the sides of a right triangle. In this case, we have an angle of 40 degrees, and we want to find the length of side AC.
2. **Identifying the Triangle**: Let’s assume that we have a right triangle where angle A is 40 degrees, and AC is the side opposite to this angle. We need the length of AC, but to calculate it, we also need the length of the hypotenuse (let’s call it AB).
3. **Using the Sin Function**: The sine of an angle in a right triangle is defined as:
sin(θ) = opposite side / hypotenuse
For our triangle, this translates to:
sin(40) = AC / AB
4. **Rearranging the Equation**: To find AC, we can rearrange the equation as follows:
AC = AB * sin(40)
5. **Calculating AC**: Now we need the value of AB (the hypotenuse) to calculate AC. Let’s assume AB measures 10 units. We can plug that into our equation:
AC = 10 * sin(40)
Using a calculator, we find that:
sin(40) ≈ 0.6428
6. **Final Calculation**: Now, substituting this value back to find AC:
AC ≈ 10 * 0.6428 ≈ 6.428
7. **Rounding Off**: Finally, rounding 6.428 to the nearest tenth gives us: 6.4.
In conclusion, if the hypotenuse AB is 10 units, the length of line segment AC, based on the equation sin(40), is approximately 6.4 units.