Question

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.

Answer 1

• 8 in

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