The perimeter of triangle ABC is 30 ft. AB = 3x+1, BC = 4x, and AC = 5x-7. List the angles of triangle ABC in order from smallest to largest. (Smallest on top, largest on bottom)(1 point) Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.

Question

The perimeter of triangle ABC is 30 ft. AB = 3x+1, BC = 4x, and AC = 5x-7. List the angles of triangle ABC in order from smallest to largest. (Smallest on top, largest on bottom)(1 point) Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.

Answer 1

Since the question is asking for the angles in the triangle to be listed from smallest to largest, we need to find a way to determine the sizes of the angles.

One way to do this is by using the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Using this information, we can set up the following inequalities:

AB + BC > AC
AB + AC > BC
BC + AC > AB

Substituting the given values, we get:

(3x+1) + (4x) > (5x-7)
(3x+1) + (5x-7) > (4x)
(4x) + (5x-7) > (3x+1)

Simplifying these inequalities gives:

7x - 6 > 5x - 6
8x - 6 > 4x - 6
9x - 6 > 3x + 1

Solving these inequalities gives:

x > 0
x > 0
x > 1/3

Since x must be greater than 1/3, we have found that there is a minimum value for x.

Now let's substitute x = 1/3 into the expressions for the sides of the triangle to find the lengths:

AB = 3(1/3) + 1 = 1 + 1 = 2 ft
BC = 4(1/3) = 4/3 ft
AC = 5(1/3) - 7 = 5/3 - 7 = -16/3 ft (negative length is not possible, so this value is invalid)

Therefore, the lengths of the sides of the triangle are:

AB = 2 ft
BC = 4/3 ft

We cannot find the length of AC using the given values, so we cannot determine the angle opposite AC. However, we can still determine the order of the angles by using the lengths of the sides that we do know.

Since the question is asking for the angles to be listed in order from smallest to largest, we can determine the order by comparing the lengths of the sides.

Since AB is the shortest side, the angle opposite AB will be the smallest angle.

Since BC is the longest side, the angle opposite BC will be the largest angle.

Therefore, the order of the angles from smallest to largest is:

angle opposite AB < angle opposite BC