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.