Thread: Trigonometry and Triangles

I have attached a picture regarding this problem. I have answered some of the parts of the problem, but I just want to know if they're right.

(a) Explain why , , and are similiar triangles

(b)What does the similiarity imply about the ratios , , and ?

(c) Does the value of depend on which triangle from part (a) is used to calculate it? Would would the value of change if it were found suing a different triangle that was similar to the three given triangles?

(d) Do your conclusions from part (c) apply to the other 5 trigonometric functions? Explain.

My answers
(a) They're similar because they share the same angle. Since they share the same angle, the lengths of each side of each of the 3 triangles should be proportional.
Is that right?

(b)The similarity implies that all three rations should have the same value as the of angle A.
Is this correct?

(c) The value of does not depend on the triangles as all the triangles are similar. The is the same if it is calculated with a different triangle that was still similar to the three triangles given as it will still have the same angle of A.
I'm not to sure about this answer? Any ideas?

(d) The conclusion from part (c) should apply to the other 5 trigonometric functions as the lengths of each side of the 3 given triangles are proportional, the trigonometric values should be the same.
Not to sure about this one either...Is it right?

My answers
(a) They're similar because they share the same angle. Since they share the same angle, the lengths of each side of each of the 3 triangles should be proportional.
Is that right?

- Almost!
Sharing the same angle puts you half way toward using the Angle-Angle (AA) rule for triangle similarity. The fact that each triangle also has a right angle finishes the job.

(b)The similarity implies that all three rations should have the same value as the of angle A.
Is this correct?

- Yup

(c) The value of does not depend on the triangles as all the triangles are similar. The is the same if it is calculated with a different triangle that was still similar to the three triangles given as it will still have the same angle of A.
I'm not to sure about this answer? Any ideas?

- You are right. As the triangles are similar, there is a scale factor that can be factored out of any of the ratios used.

(d) The conclusion from part (c) should apply to the other 5 trigonometric functions as the lengths of each side of the 3 given triangles are proportional, the trigonometric values should be the same.
Not to sure about this one either...Is it right?

- Yup. The ratios of the sides of similar shapes will all have the same scale factor that can be factored out leaving all of the trig functions working the same way.

Alright thnx alot!