Question

Given: Circle O, AO=15, OK=5, and K is a point of tangency of AK. Find: measure of angle A

Answer 1

Applying the tangent theorem and trigonometry ratio, the measure of angle A is: 19.5°.

What is the Tangent Theorem?

The tangent theorem states that if a line is tangent to a circle, the point at which the radius is drawn to the point of tangency is a right angle.

Thus, consider triangle AKO as a right triangle.

Therefore,

• angle A = reference angle
• Ok = 5 (opposite)
• AO = 15 (hypotenuse)

Using the trigonometry ratio, SOH, we have:

sin A = opp/hyp

sin A = 5/15

sin A = 0.3333

A = 19.5°

Therefore, applying the tangent theorem and trigonometry ratio, the measure of angle A is: 19.5°.

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