Solving Triangles with Law of Sines and Cosines

This video tutorial teaches how to solve triangles using the law of sines and the law of cosines. It covers when to use each law, particularly in non-right triangles, and provides two examples. The first example demonstrates solving a triangle using the law of sines, while the second example requires both the law of sines and the law of cosines. The tutorial emphasizes the importance of using original numbers to avoid rounding errors and concludes with a brief mention of the ambiguous case in triangle solving.

When is the law of sines typically applied in triangle solutions?

• When all sides are known

• When there is a right triangle

• When there is no right triangle

• When all angles are known

What is the purpose of cross-multiplying in the law of sines?

• To find the value of an unknown angle

• To calculate the area of the triangle

• To solve for the unknown side

• To verify the accuracy of given angles

How do you find the third angle in a triangle if two angles are known?

• Divide 180 by the sum of the two known angles

• Add the two known angles and subtract from 180

• Multiply the two known angles

• Add the two known angles and subtract from 360

What is the next step after finding all sides and angles in solving a triangle?

• Start another triangle problem

• Review and verify all calculations

• Check the triangle's type

• Calculate the perimeter

In which scenario is the law of cosines primarily used?

• When one side and one angle are known

• When all angles are known

• When three sides are known

• When two angles and one side are known

What does the law of cosines formula solve for in the second example?

• The height of the triangle

• The area of the triangle

• The side opposite the known angle

• The largest angle of the triangle

How do you find the sine of an angle when using the law of sines?

• Divide the side opposite by the hypotenuse

• Multiply the side opposite by the sine of the other angle

• Divide the side opposite by the side adjacent

• Cross-multiply and solve for the sine of the angle

What is the final step in solving for an angle using the law of sines?

• Multiply by the side opposite

• Take the sine inverse of the calculated value

• Divide by the cosine of the angle

• Add the results to 180 degrees

What does the ambiguous case of the law of sines involve?

• Two possible triangles

• Three possible triangles

• No possible triangles

• One possible triangle

What should you ensure before using trigonometric functions on a calculator?

• The calculator is set to radians

• The calculator is set to degrees

• The calculator has sufficient battery

• The calculator is in scientific mode