Question

Various pieces of string are cut at different lengths. Stephanie selects three pieces that measure 4.5 cm, 6 cm, and 8.5 cm. Determine what type of triangle Stephanie will form.

Answer 1

Answer:

Scalene triangle

Step-by-step explanation:

In this question, we are asked to determine what type of triangle will be formed given the length of the pieces which was used to form the triangle.

A triangle is one of the simplest shape in geometry. In fact it is one of the basic shapes that we have in geometry. It is a 3 sided polygon that contains 3 different edges or tips and 3 vertices.

According to the values in the question, we can see that the lengths of the pieces given are different. Now what does this mean for the triangle formed?

The type of triangle formed here would be a scalene triangle. A scalene triangle is a type of triangle in which all of its 3 sides have different lengths. Consequentially, the angles formed by these three sides also are different.

Answer 2

Answer:

Step-by-step explanation:

defining: a = 4.5 cm ; b = 6 cm ; c = 8.5 cm

Then by cosines law (see jpg adjunt):

$Cos(A) = \frac{b^{2} +c^{2} -a^{2} }{2bc} = \frac{6^{2} +8.5^{2} -4.5^{2} }{2*6*8} =0.862$

Apliying arcCosine(): A = 30.4°

Doing the same to B:

$Cos(B) = \frac{c^{2} +a^{2} -b^{2} }{2bc} = \frac{8.5^{2} +4.5^{2} -6^{2} }{2*4.5*8} = 0.784$

Apliying arcCosine(): B = 38.3°

Since, , B and C, has to:

A+B+C = 180° ---> C = 111.3°

This means: the triangule has two angules <90° and one >90°, wich is the definition of obtuse triangle.