Question

in triangle ABC angle B =90.angle c=30, and AB =12 cm .BD is perpendicular to AC find (1) BC ,(2) AD,(3) AC

Answer 1

BC = 20.78 cm.

AD = 6 cm.

AC = 24 cm.

Step-by-step explanation:

See the attached diagram.

If ∠ C = 30° , then ∠ A = 90° - 30° = 60°

Now, taking Δ ABC in consideration,

$\tan 30^{\circ} = \frac{AB}{BC} = \frac{12}{BC}$

⇒ BC = 20.78 cm (Answer)

Now, taking Δ ABD in consideration,

$\cos 60 ^{\circ} = \frac{AD}{AB} = \frac{AD}{12}$

⇒ AD = 6 cm. (Answer)

Again, considering Δ ABC,

$\sin 30^{\circ} = \frac{AB}{AC} = \frac{12}{AC}$

⇒ AC = 24 cm. (Answer)