If sin(y°) = cos(x°), which of the following statements is true?
a. y=w and abc ~ cde
b. y=x and abc ~cde
c. y=w and abc =~ cde
d. y=x and abc =~ cde

y = w and Δ ABC ≈ Δ CDE ⇒ answer (a)

Step-by-step explanation:

* Lets explain how to solve the problem

- Δ ABC is a right triangle

∵ m∠B = 90°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠B + z° + y° = 180°

∴ 90° + z° + y° = 180° ⇒ subtract 90° from both sides

∴ z° + y° = 90°

- sinФ = opposite/hypotenuse and cosФ = adjacent/hypotenuse

∵ sin y° = BC/AC

∵ cos z° = BC/AC

∴ sin y° = cos z°

∴ There is a fact in the right triangle if sinФ = cos∝, then Ф + ∝ = 90°

- Lets use this fact to find the answer

∵ sin y° = cos x°

∴ y° + x° = 90°

∵ y° + z° = 90°

∴ x° = z°

- Δ CDE is a right triangle

∵ m∠D = 90

∵ m∠D + x° + w° = 180°

∴ 90° + x° + w° = 180° ⇒ subtract 90° from both sides

∴ x° + w° = 90°

∵ z° + y° = 90°

∵ x° = z°

∴ y° = w°

- In Δ ABC and Δ CDE

∵ y° = w°

∵ x° = z°

∵ m∠B = m∠D

∴ Δ ABC ≈ Δ CDE

* The answer is y = w and Δ ABC ≈ Δ CDE

it has the same slope and a different y-intercept

hope this : )

step-by-step explanation: