Given right triangle ABCABC with altitude \overline{BD}

BD

drawn to hypotenuse ACAC. If AC=12AC=12 and DC=4,DC=4, what is the length of \overline{BC}

BC

in simplest radical form?

The correct answer is 4√3

Step-by-step explanation:

Consider the triangle ABC.

BC = 12 units. ∠ B = 90°. Let ∠ C = α°.

Now let us consider the triangle BDC.

DC = 4 units. ∠ D = 90°. Let ∠ C = α°.

We find here the angle C is common between both the triangles.

∴ For ΔABC, cos α° = =

and for Δ BDC, cos α° =

Now equating both the equations we get,

= 48

⇒ BC = 4√3

The length of BC is 4√3 units.

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