Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and cos ∠X = 2 and 5 tenths over 5 and 59 hundredths. see picture Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ABC. You must show all work and calculations to receive full credit. (5 points) Part B: Explain how to find the measures of segments AC and AB. You must show all work and calculations to receive full credit. (5 points)

Part A: All the trigonometric ratios of the triangles and are same.

Part B:

XY = 5

XZ = 11.18

Step-by-step explanation:

Given:

Two right angled triangles and .

is the result of dilation of by a scale factor of 2 i.e. the angles will be same but only the corresponding sides will be doubled.

i.e.

..... (1)

Part A:

To find the special relationship between the trigonometric ratios of and .

The trigonometric functions are given as:

First of all, let us consider the :

Now, let us consider the :

Using the equation (1):

All the trigonometric ratios of the triangles and are same.

Part B:

So, XY = 2.5

XZ = 5.59

Now,corresponding sides of are twice to that of .

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b