Understanding Oblique Triangles and the Law of Sines

This video tutorial covers the concept of oblique triangles, which are triangles that are not right-angled. It explains how to find the area of such triangles using trigonometric principles, specifically focusing on the Law of Sines. The tutorial also demonstrates how to solve oblique triangles by determining the measures of all sides and angles, given certain initial data. The video is divided into sections that introduce oblique triangles, explain area calculation methods, and illustrate solving techniques using the Law of Sines.

What is an oblique triangle?

• A triangle with no right angle

• A triangle with all sides equal

• A triangle with two equal angles

• A triangle with one right angle

Which formula is used to find the area of an oblique triangle?

• Sum of all sides

• One-half the product of two sides times the sine of the included angle

• One-half base times height

• Base times height

If you know angle B and sides a and c, how do you find the area of the triangle?

• One-half ab sine of B

• One-half bc sine of A

• One-half ab sine of C

• One-half ac sine of B

What is the sine of 120 degrees on the unit circle?

• 1/2

• Root 3 over 2

• Root 2 over 2

• 3/2

What is required to solve an oblique triangle using the Law of Sines?

• At least three sides

• At least two angles and one side

• At least three angles

• At least one angle and two sides

Which of the following is a valid condition to use the Law of Sines?

• Side-side-side

• Angle-side-angle

• Angle-angle-angle

• Side-side-side

In the Law of Sines, what does the ratio of side a to sine of angle A equal?

• Side b to sine of angle B

• Neither a nor b

• Both a and b

• Side c to sine of angle C

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

• Subtract the sum of the two known angles from 180 degrees

• Multiply the two known angles

• Add the two known angles

• Divide the sum of the two known angles by 2

What is the approximate length of side C if angle A is 50 degrees, angle C is 30 degrees, and side a is 10?

• 7.53

• 5.53

• 6.53

• 8.53

What is the length of side a if angle A is 98 degrees, angle C is 43 degrees, and side b is 22?

• 34.62

• 35.62

• 33.62

• 32.62