Trigonometric Problem Solving Techniques

The video tutorial introduces basic trigonometry concepts, focusing on solving triangles using the Law of Sines. It explains the Law of Sines, provides a proof, and demonstrates its application in different cases, such as angle-side-angle. The tutorial includes examples to illustrate solving triangles and emphasizes checking solutions for accuracy.

What is the primary goal when given certain information about a triangle?

• To calculate the perimeter of the triangle

• To find the lengths of the sides and the angles that are missing

• To determine if the triangle is right-angled

• To find the area of the triangle

Which law is used to find the relationship between angles and their opposite sides in any triangle?

• Law of Sines

• Law of Cosines

• Law of Tangents

• Pythagorean Theorem

In the Law of Sines, what does the ratio of the sine of an angle to its opposite side equal?

• The tangent of the angle divided by the hypotenuse

• The cosine of the angle divided by the adjacent side

• The sine of another angle divided by its opposite side

• The product of the sides of the triangle

What is the first step in proving the Law of Sines?

• Calculating the area of the triangle

• Using the Pythagorean Theorem

• Finding the hypotenuse of the triangle

• Drawing a perpendicular line from one vertex

What must be true to use the Law of Sines to solve a triangle?

• You must have two angles and one side

• You must have two sides and the included angle

• You must have one angle and one side

• You must have all three sides

In the ASA case, what is the first step to find the missing side?

• Calculate the area of the triangle

• Find the missing angle by subtracting the known angles from 180 degrees

• Use the Pythagorean Theorem

• Draw a perpendicular line from one vertex

When solving for a side using the Law of Sines, what is the easiest method to solve the proportion?

• Subtracting the ratios

• Adding the ratios

• Cross-multiplying

• Using the quadratic formula

What should you ensure about your calculator when solving trigonometric problems?

• It is in Standard mode

• It is in Scientific mode

• It is in Degree mode

• It is in Radian mode

What is a quick way to check the reasonableness of your triangle solutions?

• Ensure the shortest side is across from the largest angle

• Ensure all sides are equal

• Ensure the longest side is across from the smallest angle

• Ensure the longest side is across from the largest angle

In the second example, what is the measure of angle B?

• 108 degrees

• 49 degrees

• 38 degrees

• 23 degrees