Question

If sin(y°) = cos(x°), which of the following statements is true?

Answer 1

Answer: y = w and ΔABC ~ ΔCDE

Step-by-step explanation: Took the test and the answer was marked correct

Answer 2

Answer:

y = w and ΔABC ~ ΔCDE

Step-by-step explanation:

Given sin(y°) = cos(x°)

So, ∠y + ∠x = 90°  ⇒(1)

And as shown at the graph:

ΔABC is aright triangle at B

So, ∠y + ∠z = 90° ⇒(2)

From (1) and (2)

∴ ∠x = ∠z

ΔCDE is aright triangle at D

So, ∠x + ∠w = 90° ⇒(3)

From (1) and (3)

∴ ∠y = ∠w

So, for the triangles ΔABC and ΔCDE

• ∠A = ∠C  ⇒ proved by ∠y = ∠w
• ∠B = ∠D  ⇒ Given ∠B and ∠D are right angles.
• ∠C = ∠E  ⇒ proved by ∠x = ∠z

So, from the previous  ΔABC ~ ΔCDE by AAA postulate.

So, the answer is y = w and ΔABC ~ ΔCDE