The sides of ∠a are tangent to circle k(o) with radius r. find: oa, if r=5 cm, m∠a=60°.

The length of OA = 10 cm

Step-by-step explanation:

* Lets revise some facts about the circle

- If two tangents drawn from a point outside the circle, then

 they are equal in lengths

- The radii of the circle are perpendicular to the tangents at the

 point of tang-ency

- The line from the center to the angle between the two tangents

 bisects it

* Now lets solve the problem

∵ The sides of ∠A are tangents to circle O

∴ The radius of the circle O ⊥ to the tangent at the point of tang-ency

∴ The line OA bisects ∠A

- The measure of ∠A = 60°

∴ The measure of the angle between line OA and the tangent

  is equal to 1/2 × 60° = 30°

* Now we have right angle triangle formed from the line OA as a  

 hypotenuse two legs of the right angle one of them is the

 tangent and the other is the radius

∵ r = 5 cm

∵ The measure of the angel opposite to r is 30°

∵ OA is the hypotenuse

- By using trigonometry function

∴ sin(30°) = 5/OA

∵ sin(30°) = 1/2

∴1/2 = 5/OA ⇒ by using cross multiplication

∴ OA = 2 × 5 = 10 cm

* The length of OA = 10 cm

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step-by-step explanation:

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step-by-step explanation: