Question

1. Two segments from P are tangent to circle o. If angle P = 60 and the radius of circle o is

12 feet, find the length of each tangent.

Answer 1

20.7 ft each

Explanation:

See the diagram attached below which describes and represents the information given to us.

The tangents are PA and PB.

Tangents form right angle with the radius of a circle, therefore:

<OBP = <OAP = 90°

Therefore ∆OBP is a right triangle.

m<APO = m<BPO = ½(60) = 30°

Thus, in ∆OBP,

Reference angle = 30°

Side length opposite to reference angle = 12 ft

Adjacent length = length of tangent PB

Apply trigonometric function TOA, to find PB:

Tan 30 = Opp/Adj

Tan 30 = 12/PB

PB × Tan 30 = 12

PB = 12/Tan 30

PB = 20.7846097 ≈ 20.7 ft (nearest tenth)

Length of each segment = 20.7 ft