One, Two, Or No Triangles (How Can You Tell)

The video tutorial addresses the common student struggle with understanding when one, two, or no triangles exist in the ambiguous case of side-side-angle (SSA) triangle problems. It begins by explaining right triangles and the use of the sine function to find height. The tutorial then shifts focus to oblique triangles, detailing conditions for no triangle, one triangle, and two triangles based on side length comparisons. The importance of practice in mastering these concepts is emphasized, and the video concludes with a reminder that the ambiguous case only applies to SSA scenarios.

What is the relationship used to find the height of a right triangle?

• Secant of angle equals hypotenuse over adjacent

• Tangent of angle equals opposite over adjacent

• Cosine of angle equals adjacent over hypotenuse

• Sine of angle equals opposite over hypotenuse

In an oblique triangle, if the third side is shorter than the height, what is the result?

• A right triangle is formed

• Two triangles exist

• One triangle exists

• No triangle exists

When does exactly one triangle exist in an oblique triangle scenario?

• When the third side is equal to the height

• When the third side is less than the height

• When the third side is greater than the hypotenuse

• When the third side is less than the hypotenuse

What is the condition for two triangles to exist in an oblique triangle?

• The third side is less than the height

• The third side is greater than the hypotenuse

• The third side is greater than the height but less than the hypotenuse

• The third side is equal to the hypotenuse

In which scenario does the ambiguous case not apply?

• Side-angle-side

• Angle-side-angle

• Angle-angle-side

• Side-side-angle