Question

A connecting of rod 24 inches in length is attached at Q to a drive wheel whose radius is 6 in. when OP, the distance from P to the center of the wheel, is 26 inches, find the angle QOP.

Answer 1

Answer on Question #77612 – Math – Trigonometry

Question. A connecting of rod 24 inches in length is attached at Q to a drive wheel whose radius is 6 in. when OP, the distance from P to the center of the wheel, is 26 inches, find the angle QOP.

Solution. By law of cosines:

$$Q P ^ {2} = O Q ^ {2} + O P ^ {2} - 2 * O Q * O P * \cos \widehat {Q O P}$$

From this we can extract $\cos \widehat{QOP}$ :

$$\cos \widehat {Q O P} = \frac {O Q ^ {2} + O P ^ {2} - Q P ^ {2}}{2 * O Q * O P}$$

Calculations:

$$\cos \widehat {Q O P} = \frac {6 ^ {2} + 2 6 ^ {2} - 2 4 ^ {2}}{2 * 6 * 2 6} = \frac {1 3 6}{3 1 2} = \frac {1 7}{3 9}$$

Now we can write the answer:

$$\widehat {Q O P} = \arccos \frac {1 7}{3 9}$$

Answer: $\widehat{QOP} = \arccos \frac{17}{39}$ .

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