Solving Angle & Triangle Problems: 2Tsin(angle) = 3mg

• Lavace
In summary, the conversation discusses a method for solving a question involving tan(angle) = 3/4. Instead of using the inverse tangent function and risking loss of accuracy, the teacher suggests rounding off the angle and using pythagorean theorem to find the missing side of the triangle. This results in sin(angle) = 3/5 and cos(angle) = 4/5. The conversation ends with the question of how to apply this method to the given statement of 2Tsin(angle) = 3mg?

Lavace

THis isn't exactly a question however, its a method my teacher talked to me about and I don't quite understand.

This is a way of getting greater accuracy, and attaining the higher grades.

The question states, tan(angle) = 3/4
So instead of using tan^-1 (3/4) to get the angle with many digits, round it off and losing accuracy, she said:

Drawing the triangle out results in:
http://imgplace.com/directory/dir51/1172694216_triangle.JPG
Using pythag you can work out the other side.

Now you have:
sin(angle) = 3/5
cos(angle) = 4/5

I have worked out the statement:
2Tsin(angle) = 3mg

However, how do I apply what was attained from the triangle to this question?
Thanks.

2T*3/5=3mg?

I would recommend using the trigonometric identities to solve this problem. First, we can rewrite the equation as 2Tsin(angle) = 3mg as 2Tsin(angle) - 3mg = 0. Then, we can use the identity sin^2(angle) + cos^2(angle) = 1 to substitute for sin(angle) and cos(angle) in terms of the given value of tan(angle). This will result in a quadratic equation, which can be solved using the quadratic formula or by factoring. Once the value of angle is determined, it can be substituted back into the original equation to solve for T. Additionally, drawing out the triangle and using the Pythagorean theorem is a helpful visual aid, but it is important to also use the appropriate mathematical methods to solve the problem accurately.

1. What does the equation 2Tsin(angle) = 3mg represent?

The equation 2Tsin(angle) = 3mg represents the force balance in a system where a mass (m) is hanging from two ropes with tension (T) at an angle (angle) with respect to the vertical direction. The left side of the equation represents the horizontal component of the tension force, while the right side represents the weight of the mass.

2. How do you solve for the angle in this equation?

To solve for the angle, you can rearrange the equation to isolate the sine of the angle. This would give you sin(angle) = (3mg)/(2T). Then, you can use the inverse sine function to find the value of the angle.

3. Can this equation be used for any triangle or only right triangles?

This equation can be used for any triangle, as long as the sides and angles are measured correctly. The sine function can be applied to any angle, not just right angles.

4. How does changing the mass or tension affect the angle in this equation?

Changing the mass or tension will affect the value of the angle in this equation. As the mass increases, the angle will decrease, and as the tension increases, the angle will also decrease. This is because the weight of the mass and the tension force have a direct relationship with the sine of the angle, as shown in the equation.

5. Are there any real-world applications for this equation?

Yes, this equation has many real-world applications, such as determining the angle of a hanging object, calculating the forces acting on a bridge or tower, and analyzing the forces involved in a pulley system. It is commonly used in engineering, physics, and other scientific fields.