Atriangle has two congruent sides that measure 8.7 cm and 12.3 cm. which could be the measure of the third side

Option C. 15 cm

Step-by-step explanation:

The correct question is

A triangle has two sides that measure 8.7 cm and 12.3 cm. Which could be the measure of the third side?

A.2.6 cm

B.3.6 cm

C.15 cm

D.21 cm

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Analyze two cases

Let

x > the length of the third side

First case

x+8.7 > 12.3

x>12.3-8.7

x> 3.6 cm

Second case

12.3+8.7 > x

21 > x

Rewrite

x < 21 cm

the parent function for this case is:

f (x) = cos (x)

we apply the following transformations:

reflections:

to graph y = -f (x), reflect the graph of y = f (x) on the x-axis.

we have then:

f (x) = -cos (x)

expansions:

to graph y = a * f (x)

if 0 < a < 1, the graph of y = f (x) is compressed vertically by a factor a

we have then:

f (x) = -0.1cos (x)

vertical translations :

suppose that k> 0

to graph y = f (x) -k, move the graph of k units down.

we have then:

f (x) = -0.1cos (x) -4

answer:

b

reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down