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which best describes the triangle or the triangles, if any, that can be formed with two sides that measure 5 inches and an angle that measures 60 degrees?

two different isosceles triangles
no triangle
one isosceles triangle
one equilateral triangle

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Answer with explanation:

Suppose the two sides of triangle are, 5 inches and angle between the two sides is 60 degrees.

We will use cosine formula to find third side.Let side opposite to angle having measure 60 degree, is equal to a inches.

[tex]cos 60^{\circ}=\frac{b^2+c^2-a^2}{2 b c}\\\\  \frac{1}{2}=\frac{5^2+5^2-a^2}{2\times 5 \times 5}\\\\25=50-a^2\\\\a^2=50-25\\\\a^2=25\\\\a=\pm 5[/tex]

Omitting, a= -5, because side can't be negative.

So, third side = 5 cm.

Means, triangle is equilateral.

If angle between , two sides having measure 5 cm , is not 60 degree, then the triangle will be always Isosceles.

we will sine rule to find remaining measurements.

[tex]\frac{5}{\sin60^{\circ}}=\frac{5}{\sin B^{\circ}}=\frac{c}{\sin C^{\circ}}\\\\B=60^{\circ}\\\\ \text{by angle sum property of triangle}\\\\ C=60^{\circ}\\\\ \text{Side}\rightarrow c=5[/tex]

In this case,also ,triangle is equilateral.

Option D: one equilateral triangle

Ver imagen Аноним

The triangle is one equilateral triangle.

Answering this question means we have to know the major types of triangles.

They are;

  • Isosceles triangles ; This type has 2 equal sides and 2 equal angles

  • Scalene triangle; This type has 3 sides with all having different measurement as well as 3 different angles.

  • Equilateral triangle; This type has 3 equal sides and the 3 angles equal to 60°.

      Now, from the question, we are told that two sides measure 5 inches and an angle that measures 60°.

  • Since 2 sides of the triangle are equal, it means at least 2 of the angles must be equal. Since one angle is already 60°, it means that another angle must be 60°.

  • Sum of angles in a triangle is 180°, it means that the third angle is;

        180° - (60° + 60°) = 60°

  • This means that, the triangle has 3 equal internal angles of 60° and this corresponds to the definition of an equilateral angle.

Thus, the triangle is one equilateral triangle.

Read more at; brainly.com/question/14993166

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