What is the formula for isolating b in the law of sines?

Thread starter bobsmith76
Start date Aug 23, 2011
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Law Law of sines

In summary, the law of sines is a mathematical formula used in trigonometry to solve for unknown sides and angles in a triangle. It is commonly used in real-world applications such as navigation, engineering, and astronomy. The formula for isolating b in the law of sines is b = (sin(B) * a) / sin(A), and to solve for b, you need to know at least two angles and one side of the triangle. However, the law of sines has limitations, as it can only be used in non-right triangles and may produce inaccurate results if there is a measurement error.

Aug 23, 2011

bobsmith76

sin α/a = sin β/b

when my isolates b they get

b = α sin β/sinα

I would think to isolate b you would multiply both sides by 1/sinβ which would make

b = sin α/ a sin β

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Aug 23, 2011

pwsnafu

Science Advisor

Take sin α/a = sin β/b.

Multiply both sides by 1/sinβ and you get

sin α / (a sin β) = 1/b.

Related to What is the formula for isolating b in the law of sines?

1. What exactly is the law of sines?

The law of sines is a mathematical formula used in trigonometry to solve for the unknown sides and angles of a triangle. It states that the ratio of the length of a side to the sine of its opposite angle is equal to the ratio of the length of another side to the sine of its opposite angle.

2. How is the law of sines useful in real-world applications?

The law of sines is commonly used in navigation, engineering, and astronomy to calculate distances and angles. It is also used in surveying and map-making to determine the location and height of objects.

3. What is the formula for isolating b in the law of sines?

The formula for isolating b in the law of sines is b = (sin(B) * a) / sin(A), where b is the unknown side, A and B are the angles opposite to sides a and b respectively, and a is a known side.

4. How do you use the law of sines to solve for b?

To solve for b, you need to know at least two angles and one side of the triangle. Then, plug the values into the formula b = (sin(B) * a) / sin(A) and solve for b using basic algebraic operations.

5. Are there any limitations to using the law of sines?

Yes, the law of sines can only be used to solve for unknown sides and angles in non-right triangles. It also assumes that the given angles and sides are accurate, and may produce inaccurate results if there is a measurement error. Additionally, the law of sines does not work if all three angles are unknown.