SOLUTION: Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB, XY = 2.5, and ZX = 5.59. Part A: Find cos < X. Explain how cos <X compares to cos <A. Part B: Find AC and

Algebra ->  Triangles -> SOLUTION: Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB, XY = 2.5, and ZX = 5.59. Part A: Find cos < X. Explain how cos <X compares to cos <A. Part B: Find AC and      Log On


   

Question 1206864: Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB, XY = 2.5, and ZX = 5.59.
Part A: Find cos < X. Explain how cos Part B: Find AC and BA. You must show all work and calculations to receive full credit.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


Part A: Find cos
assuming you need to find
cos%28X%29
using formula cos%28X%29=adj%2Fhyp+

In triangle XYZ, XY is the adjacent side to angle X, and ZX is the hypotenuse.
we are given adj=2.5 and hyp+=5.59
cos%28X%29=2.5%2F5.59
cos%28X%29=0.447
now, compare cos%28X%29+to cos%28A%29+in triangle ABC

since ABC is dilated from triangle XYZ by factor 2, we know that triangles XYZ and ABC are similar, and corresponding angles are congruent
so cos%28X%29=cos%28A%29=0.447


Part B: Find AC and BA.
Given the scale factor of 2, the corresponding sides of triangle ACB are twice the length+of triangle XYZ}.
So,
AC+=+2+%2A+XY+=+2+%2A2.5+=+5
BA+=+2+%2AZX+=+2%2A5.59+=+11.18


Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.

As it is given in the post, cosine of the angle < X CAN NOT be found: there is no enough data for it.

@MathLover1 assumed in her solution that triangle XYZ is a right-angled triangle,
but it is not given in the post,

so, there is no base for this assumption.