Question

Select all the choices that apply to A B C with: ∠A=61°, ∠B=48°, AB=100. Options:

A) Obtuse
B) Acute
C) Scalene
D) Isosceles
E) SSA
F) ASA
G) SAS
H) SSS

Answer 1

The triangle characterized with angles ∠A=61° and ∠B=48° and side AB=100 is acute, scalene, and fits the SSA description. The information given does not apply to ASA, SAS, SSS, obtuse, or isosceles classifications.

Step-by-step explanation:

The question provided involves classifying a triangle with given information about its angles and sides. Given the angles ∠A = 61° and ∠B = 48°, and the side AB = 100, we can deduce several characteristics of this triangle:

• Acute: All the angles given are less than 90°, so the triangle is acute.
• Scalene: Since there is no information indicating that any sides are equal, we assume it is scalene.
• SSA: The given information side-side-angle corresponds to the SSA condition, which is not a congruence criterion but is a way to describe the information we have about the triangle.
• ASA and SAS: These are both criteria for triangle congruence. ASA (angle-side-angle) is not applicable because we only have one side length and two non-sequential angles. SAS (side-angle-side) does not apply because we do not have an angle included between two known sides.
• SSS: We can't confirm that this applies because we only know the length of one side.
• Obtuse and Isosceles: With the information given, we cannot claim the triangle is obtuse (no angle is greater than 90°) or isosceles (we do not have any known equal sides).

To classify this triangle correctly, select options B) Acute, C) Scalene, E) SSA.