Understanding the Ambiguous Case in Triangles

What is the first step in identifying the number of possible triangles in the ambiguous case?

• Calculate the area of the triangle.

• Check if the given angle is a right angle.

• Determine if the given angle is obtuse or acute.

• Use the Pythagorean theorem.

In an obtuse triangle, what condition leads to no triangle being possible?

• The side adjacent to the obtuse angle is the longest.

• The side opposite the obtuse angle is the longest.

• The side opposite the obtuse angle is the shortest.

• The side adjacent to the obtuse angle is the shortest.

What happens if the side opposite an acute angle is shorter than the altitude?

• A right triangle is formed.

• Two triangles are possible.

• No triangle is possible.

• Only one triangle is possible.

What is the result when the side opposite an acute angle is exactly the same length as the altitude?

• A right triangle is formed.

• An isosceles triangle is formed.

• No triangle is possible.

• Two triangles are possible.

How do you determine the height in a triangle problem using the law of sines?

• By using the sine of the angle.

• By using the secant of the angle.

• By using the tangent of the angle.

• By using the cosine of the angle.

In the example problem, what is the calculated angle C in the first triangle?

• 93.6 degrees

• 26.4 degrees

• 123.6 degrees

• 56.4 degrees

What is the significance of having two sides congruent in a triangle?

• It forms a scalene triangle.

• It forms an isosceles triangle.

• It forms a right triangle.

• It forms an equilateral triangle.

How do you solve for the third angle in a triangle once two angles are known?

• Add the two angles and subtract from 180 degrees.

• Add the two angles and subtract from 360 degrees.

• Divide the sum of the two angles by 2.

• Multiply the two angles and subtract from 180 degrees.

What is the calculated length of side B in the second triangle?

• 10.7

• 24.0

• 12.0

• 20.0

What is the next topic suggested for further learning after understanding the ambiguous case?

• Law of Cotangents

• Law of Tangents

• Law of Cosines

• Law of Secants