Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and tan ∠X = 5 over 2 and 5 tenths. Triangles XYZ and ACB; angles Y and C both measure 90 degrees, angles A and X are congruent.

Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ACB. 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 CB. You must show all work and calculations to receive full credit. (5 points)

cosx=2.5/5.59

   "   =.4472

 "x"  =63.434°; so "a" is=.

When talking about triangles and a scale; the angles remain=. In this case; "a" and "x"; y=c; z=b.

The sides are 2x or x/2.

Part A: Dilation proportionately changes side lengths, but it does not change the angle sizes. Therefore, the triangles are similar triangles.

Dilation means the triangle ΔXYZ was stretched by a factor of "2".

m∠Y = m∠C = 90º ← given

ΔXYZ and ΔACB are the right triangles.

∠X ≅ ∠A ← given

∠X and ∠Z are complementary angles

m∠Z = 90° - m∠X

∠A and ∠B are complementary angles

m∠B = 90° - m∠A

Therefore, ∠Z ≅ ∠B

ΔXYZ ∼ ΔACB → similar triangles: corresponding sides are proportional, corresponding angles are congruent

sin∠X = 5/5.59 ← given

sin∠X = YZ/XY

YZ = 5 (units) → leg in ΔXYZ

XZ = 5.59 (units) → hypotenuse in ΔXYZ

Calculating the length of leg XY:

XY = √((5.59)2 - 52) ≅ 2.4996 (units)

CB/YZ = 2 ← given

CD = 2YZ = 2 • 5 = 10 (units)

AC/XY = 2 ← given

AC = 2XY ≅ 2 • 2.4996 ≅ 4.999 (units)

Step-by-step explanation:

29.5977692753

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: