Sine Law Ambiguous

Two Triangles

One Triangle

None

$$49\degree$$

$$29\degree$$

$$49\degree$$ and $$131\degree$$

$$29\degree$$ and $$151\degree$$

no triangle possible

B = 14^o, C = 21^o, c = 8.7

B = 52^o, C = 102^o, c = 11.2

B = 52^o , C = 102^o, c = 11.2

OR

B = 128^o, C = 26^o, c = 5.0

10

8

6.1

4.9

$$58\degree$$

$$61\degree$$

$$78\degree$$

$$74\degree$$

12

10

23

14

$$50\degree$$

$$60\degree$$

$$78\degree$$

$$74\degree$$

A scenario where only right triangles are involved

A case where no triangle exists

A situation where two different triangles could satisfy the given conditions

A condition where all angles are known but no sides

To solve oblique triangles

To calculate the hypotenuse of a right triangle

To find the radius of a circle

To define the relationship between the sides and angles of a parallelogram

Measuring the height of a building using a right triangle

Determining the volume of a sphere

Calculating the circumference of a circle

Finding the area of an oblique triangle using the sine function