Which of the following measures would create two possible triangles? Answer Choices: three angles: 26°, 48°, and

Which of the following measures would create two possible triangles?

Answer Choices:
three angles: 26°, 48°, and 106°
three sides: 5 cm, 9 cm, and 15 cm
an angle of 48° found between two sides: 4 cm and 6 cm
two sides, 4 cm and 6 cm, with an angle of 48° not found between them

2 thoughts on “Which of the following measures would create two possible triangles? Answer Choices: three angles: 26°, 48°, and”

  1. Answer:
    Below in bold.
    Step-by-step explanation:
    The three angles of a triangle add up to 180 degrees.
    106 + 26 + 48 = 180
    So this will give a triangle.
    In a triangle, the sum of any 2 of the sides must be greater that the other side.
    So,  in the case of sides 5,  9 and 15 cm ,  5 + 9 < 15 so these
    will not give a triangle.
    An angle of 48 between sides 4 and 6 cm:
    Using the Cosine Rule to find the other side x:
    x^2 = 4^2 + 6^2 – 2.4.6cos48
    x^2 = 18.88 so x = 4.46 cm
    So the 3 sides are 4 , 4.5 and 6 cm long
    this will make a triangle
    An angle not betweem side  of 4 and side of 6/
    applying sine rule:
    4 /sin 48 = 6 / sin x
    sin x = 5 sin 48 / 4 = 1.1147
    As yhe sine of an angle must b between – 1 and 1 no angle is possible so no trangle can be draw.

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  2. The answer is three angles: 26°, 48°, and 106°

    because the interior angles of a triangle must always add up to 180°:
    26 + 48 + 106 = 180 ✅

    Reply

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