If you're studying trigonometry, you may come across a problem that requires you to find the acute angle between two lines. This can be a bit challenging, but with the right knowledge and tools, you can solve it easily. In this article, we'll explain how to find the acute angle between the lines and round your answer to the nearest degree.
What are Lines?
In geometry, a line is defined as a straight path that extends infinitely in both directions. Lines are used to represent many things, such as boundaries, borders, and paths. In mathematics, lines are often used to solve equations and problems.
What is an Acute Angle?
An acute angle is an angle that measures less than 90 degrees. It is often represented by a small arc with a dot in the middle. Acute angles are common in geometry and trigonometry, and they are used to measure the angles between lines, planes, and other objects.
How to Find the Acute Angle Between Two Lines?
When you have two lines and you want to find the acute angle between them, there are several steps you need to follow:
- Determine the slopes of the two lines.
- Calculate the angle between the slopes using the formula: tan(theta) = |(m1 - m2) / (1 + m1*m2)|, where m1 and m2 are the slopes of the lines.
- Convert the angle from radians to degrees using the formula: degrees = radians * (180/pi).
- Round the answer to the nearest degree.
Example Problem:
Let's say you have two lines with the equations y = 2x + 3 and y = -0.5x + 4. To find the acute angle between them, you need to determine their slopes:
slope1 = 2, slope2 = -0.5
Next, use the formula to calculate the angle between the slopes:
tan(theta) = |(m1 - m2) / (1 + m1*m2)| = |(2 - (-0.5)) / (1 + 2*(-0.5))| = 1.5/0.5 = 3
Now, convert the angle from radians to degrees:
degrees = radians * (180/pi) = 1.249 * (180/pi) = 71.57
Finally, round the answer to the nearest degree:
The acute angle between the two lines is 72 degrees.
Conclusion
Finding the acute angle between two lines may seem daunting at first, but with practice, it becomes easier. Remember to follow the steps outlined in this article, and you'll be able to solve these types of problems in no time.
