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Please use statement and reason, not sin cos or tan. In rectangle ABCD the diagonals intersect each other at point O and ABD = 30. Find BC if AC = 16 in. Include a picture if you can, but you don't have to.

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mhanifa

Answer:

  • 8 in

Step-by-step explanation:

  • Rectangle has properties:
  • Diagonals are congruent
  • Opposite sides are congruent
  • All angles are right

Given

  • m∠ABD = 30°
  • AC = 16 in
  • BC = ?

Solution

As per properties mentioned above we have:

  • BC = AD
  • BD = AC = 16 in

ΔABD is right triangle with ∠B - 30°, ∠A- 90°, ∠D - 60°

Side opposite to 30 is half of the length of the hypotenuse

AD is opposite to ∠B and BD is the hypotenuse, then:

  • AD = 1/2*BD
  • AD = 1/2(16)
  • AD = 8 in

and

  • BC = AD = 8 in

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