Which of the following measures would produce TWO possible triangles?

two sides of 4 cm and 7 cm with an angle of 54° not between those two sides
two sides of 4 cm and 7 cm with an angle of 54° between those two sides
three angles: 62°, 34°, and 84°
three sides: 4 cm, 7 cm, and 9 cm

Answer:

The two possible measures tobproduce a ️ are ''Three angles: 62, 32°, and 84°" & "Three sides: 4cm, 7cm, and 9cm"

The triangle is formed by two sides of 4 cm and 7 cm with an angle of 54° between those two sides

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Two sides of 4 cm and 7 cm with an angle of 54° between those two sides would produce two possible triangles.

This is because if the angle is between the two sides, the two sides can be positioned in two different ways to form two distinct triangles, whereas if the angle is not between the two sides, only one triangle can be formed.

The other measures listed do not provide enough information to determine if there are one or two possible triangles.

Hence , the triangle is solved

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