Question

Given right triangle ABCABC with altitude \overline{BD}

Answer 1

Answer:

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° = $\frac{BC}{AC}$ = $\frac{BC}{12}$

and for Δ BDC, cos α° = $\frac{DC}{BC} = \frac{4}{BC}$

Now equating both the equations we get,

$BC^{2}$ = 48

⇒ BC = 4√3

The length of BC is 4√3 units.