Cosine Rule Help: Solving the Cut Size of a Curved Bar

• Con Air
In summary, the person is seeking help with calculating the cut size of a curved bar at work. They have the chord length and radius, and need to use the cosine rule and arc length formula to find the inner angle and resulting arc length. They were able to get a solution of 28.17° and 656.6mm, but had some doubts about the accuracy and thanked the expert for their help.

Homework Statement

Hello! I've run into a problem at work and need a quick solution! Basically I need to work out the cut size of a curved bar. I have the chord length (650mm) and the radius' (1335mm) Obviously i need to calculate the inner most angle, then multiply my diameter by pi, divide by 360 then multiply by my new found angle to find arc length

Homework Equations

Cosine rule A=b$^{2}$+c$^{2}$-a$^{2}$$/$2bc

C=∏d

The Attempt at a Solution

obviously c and b are both equal at 1335mm. so the triangle becomes isosceles

Arc length = ∏x2670/360 x (1335$^{2}$+1335$^{2}$- 650$^{2}$/2x1335x1335)$^{cos-1}$

this equation leaves us at 28.17°

then (2670x∏/360)x28.17=656mm

Only 6mm gain on the arc? is this normal? please help!

many thanks, connor.

I get 656.6 mm. You did it correctly.

thanks very much, I've never applied that sort of trigonometry to my work before, i was abit unsure! thanks very much for your help.

1. What is the Cosine Rule?

The Cosine Rule, also known as the Law of Cosines, is a mathematical formula used to find the length of a side or an angle of a triangle. It is based on the relationship between the sides and angles of a triangle, specifically the cosine of an angle and the length of the opposite side.

2. How is the Cosine Rule used to solve the cut size of a curved bar?

The Cosine Rule can be used to find the length of the curved bar by treating it as one side of a triangle. The other two sides can be determined by measuring the distance from the endpoints of the curve to the center of the curve. The angle between these two sides can be calculated using the Cosine Rule, and then the length of the curved bar can be found using the same formula.

3. What are the steps to using the Cosine Rule to solve for the cut size of a curved bar?

The steps are as follows:
1. Measure the distance from the endpoints of the curve to the center of the curve.
2. Use the Cosine Rule to find the angle between these two lines.
3. Once you have the angle, use the Cosine Rule again to find the length of the curved bar.

4. Are there any special cases where the Cosine Rule cannot be used to solve for the cut size of a curved bar?

Yes, the Cosine Rule can only be used for solving triangles. If the curved bar is not part of a triangle, then the Cosine Rule cannot be applied. Additionally, the Cosine Rule may not be accurate if the curved bar has a complex shape or is not symmetrical.

5. Can the Cosine Rule be used to solve for the cut size of a curved bar in any units of measurement?

Yes, the Cosine Rule can be used with any unit of measurement as long as all measurements are consistent. For example, if the distance from the endpoints of the curve to the center of the curve is measured in inches, then the length of the curved bar should also be measured in inches. This will ensure accurate results when using the Cosine Rule.