Question

The sides of ∠A are tangent to circle k(O) with radius r. Find:
OA, if r=5 cm, m∠A=60°.

Answer 1

Answer:

OA=5.77 cm

Step-by-step explanation:

The sides of ∠A are tangent to circle k(O) with radius r.

Please find the  attached file fir figure.

OM=r = 5 cm

OM perpendicular to AM because radius perpendicular to tangent.

In ΔOAM, ∠AMO=90°

$\sin\angle A=\dfrac{OM}{OA}$

$\sin 60^\circ=\dfrac{5}{OA}$

$OA=5\csc60^\circ=5.77$

Hence, The length of OA is 5.77 cm.