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


triangles ABC and CDE in which angles B and D are right angles, point E is between points A and C, the measure of angle A is y degrees, the measure of angle E is x degrees, the measure of angle DCE is w degrees, and the measure of angle ECB is z degrees


y = w and ΔABC ~ ΔCDE

y = x and ΔABC ~ ΔCDE

y = w and ΔABC ≅ ΔCDE

y = x and ΔABC ≅ ΔCDE

If siny cosx which of the following statements is truetriangles ABC and CDE in which angles B and D are right angles point E is between points A and C the measu class=

Respuesta :

Matheng

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

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