Question

Given circle D, calculate the measure of arc AC if AD=16 and BD=13.

Answer 1

18.66

Explanation:

Using the pythagorean theorem:

a^2 + b^2 = c^2

a^2 + 13^2 = 16^2

a^2 + 169 = 256

a^2 = 87

a = 9.33

Since we need to figure out length AC and not just AB, we can multiply our answer by 2:

9.33 x 2 = 18.66

Answer 2

71.32°

Explanation:

The measure of angle ADB can be found using the trig relation ...

Cos = Adjacent/Hypotenuse

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cos(ADB) = DB/AD = 13/16

Using the inverse function, ...

∠ADB = arccos(13/16) ≈ 35.659°

Arc AC has the same measure as angle ADC, which is double the measure of angle ADB.

Arc AC = 2×35.659° = 71.318° ≈ 71.32°

The measure of arc AC is about 71.32°.

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Additional comment

The length of arc AC is the product of the radius and its radian measure:

length AC = (16)(71.32π/180) ≈ 19.92 . . . units