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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

$$\sin \frac{\theta}{2} = \frac{\frac{70}{2}}{40}$$

$$\theta =2 \sin^{-1} \frac{35}{40}$$

$$\theta = 122.09^o$$