Fill in the blank with the correct response.

x=4

Step-by-step explanation:

Notice that the angle between side x and side 2 in the small right triangle on the left is the same angle between the sides x and (2+6 = 8) in the larger right angle triangle.

if we name the angle in question , then we have for the small triangle on the left, the following trigonometric relationship:

because in that small triangle, the side adjacent (adj) to angle  is "2" and the hypotenuse (hyp) is "x" .

We can set some similar relationship for the larger triangle, which has a hypotenuse (hyp)  of length (2+6 = 8), and that has for side adjacent (adj) to the angle side "x":

Now, we can make both expressions equal since they involve the same angle, and solve for "x" in the resultant formula:

therefore x is either "4" or "-4" to give 16 when squared.

We opt for the positive answer since we want a length.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

2

step-by-step explanation: