Question

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and tan ∠X = 5 over 2 and 5 tenths.
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.

Part B: Explain how to find the measures of segments AC and CB. You must show all work and calculations to receive full credit.

Answer 1

Hi, I will be answering your question, do you have any questions for me off the start?

Answer 2

yes, how exactly do i solve trigonometric ratios ?

Answer 3

Well, you will be using this Equation;
\[\sin \theta=\frac{ a }{ h }\]
Could you go further into explaining what you need help with?

Answer 4

well i dont know how to solve the question

Answer 5

Okay, so;
\[\theta=\]
Angle Theta

\[a=\]
Length of the opposite side a

\[h=\]
Length of hypotenuse h

Does that help a little?

Answer 6

yes a little, but what numbers do i put for a and h ?

Answer 7

I will give you some formulas that are labeled.
" b mid-length
" c hypotenuse
angle "a" which is the (alpha) opposite side a
" β(beta) " " b
" y(gamma) " " c
The major formal you're going to want to use to solve this equation is:
\[a^2+b^2=c^2\]

Answer 8

As for solving <ACB; the angle is y which is a right angle.

Answer 9

Now, Given that:
\[\tan<x=\frac{ 5 }{ 2 }+\frac{ 1 }{ 2 }=\frac{ 6 }{ 2 }=3atan=71.565=\beta \]
That meaning :
\[a=18.44\]
Also given,
\[y=rt~<\]
To get the sides use the formulas, use both:
\[a^2+b^2=c^2\]
&
\[a/\sin~a=b/\sin \beta=c~\sin~y\]
Also, Remeber:
\[a+\beta+y=180^{o}\]

Answer 10

@snowflake0531- your thoughts, please.
tyvm

Answer 11

the 'special relationship' is just that they're similar, and that the sides are proportional to one another, I think
Because with proportional sides and equal angles, the fraction on the other side of the equal sign reduces/simplifies to the other fraction, in simpler form.
For example, if itwas sin(35) = 5/7, and the other triangle's equation was sin(35) = 10/14, it simplifies to 4/6, and so it proves that the sides are proportional

So for Par tA to prove ^^^^
Just take the sin, cos, or tangent, doesn't really matter which, but then do the same sin/cos/tan with the other triangle to prove that the equation ends up being the same, I think o-O