Trigonometry Solutions
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The radius of a circle is 40 inches, the length of the chord is 70 inches. Find the central angle subtended by the chord.
Solution 1. Solution by cosine law
\(70^2 = 40^2 + 40^2 - 2(40)(40) \cos \theta \)
\(\theta = \cos^{-1} \frac{70^2-40^2-40^2}{-2(40^2)}\)
\(\theta = 122.09^o\)
Solution 2. Solution by right triangle
\(\sin \frac{\theta}{2} = \frac{\frac{70}{2}}{40} \)
\(\theta =2 \sin^{-1} \frac{35}{40}\)
\(\theta = 122.09^o\)