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Name Date 9.7 Law of Sines and Law of Cosines For use with Exploration 9.7 Essential Question What are the Law of Sines and the Law of Cosines? 1 EXPLORATION: Discovering the Law of Sines Go to BigIdeasMath.com

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How to fill out law of sines and

01

To fill out the law of sines, you will first need to identify the given components of a triangle. These components include the lengths of the sides and the measures of the angles.

02

Next, determine if you have enough information to use the law of sines. The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. In order to use this law, you need to have either two angles and one side length, or two side lengths and one angle measurement.

03

If you have enough information, set up the equation using the law of sines. The equation is written as: sin(A)/a = sin(B)/b = sin(C)/c, where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.

04

Substitute the known values into the equation and solve for the unknown side or angle. Use algebraic methods to rearrange the equation and isolate the variable you are looking for.

05

Calculate the value of the unknown side or angle using a calculator or trigonometric table if necessary.

06

Repeat steps 3-5 if you have more than one unknown side or angle, until you have filled out all the missing values in the triangle.

07

Double-check your answers by ensuring that the ratios on both sides of the equation are equal.

08

Finally, label each side and angle in the triangle with its corresponding measurement to complete the fill-out process of the law of sines.

Who needs the law of sines?

01

Students studying trigonometry and geometry often need to use the law of sines to solve problems related to triangles. This could include finding missing side lengths or angle measurements.

02

Architects and engineers may also utilize the law of sines when designing structures that involve triangles, such as building roofs, bridges, or support systems.

03

Additionally, surveyors and cartographers may employ the law of sines to measure distances or map out land features, especially when working with irregularly shaped regions that can be approximated as triangles.

In summary, anyone who works with triangles or has a need to solve problems involving the relationships between sides and angles in a triangle can benefit from understanding and using the law of sines.

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What is law of sines and?

The law of sines relates the sides of a triangle to the sines of its angles.

Who is required to file law of sines and?

Anyone studying trigonometry or geometry may be required to use the law of sines.

How to fill out law of sines and?

To fill out the law of sines, you need to know at least one side and one angle of a triangle.

What is the purpose of law of sines and?

The purpose of the law of sines is to calculate unknown sides or angles in a triangle.

What information must be reported on law of sines and?

You must report at least one side and its corresponding angle or two sides and a non-included angle.

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