Explained: "Find the lengths a, b, c, and d..." - Plainmath

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Tahmid Knox

Answered question

2021-04-30

Find the lengths a, b, c, and d in the following figure:

Answer & Explanation

Tuthornt

Skilled2021-05-02Added 107 answers

First find PQ and QR. For PQ, use the right-triangle:

\tan (24^{\circ}) = \frac{1}{P Q}

, so

P Q = \frac{1}{\tan (24^{\circ}}}

For QR, first find its opposite angle to be

180^{\circ} - 24^{\circ} - 48^{\circ} = 108^{\circ}

Now using the law of sines:

\frac{\sin (108^{\circ})}{Q R} = \frac{\sin (24^{\circ})}{2}

, thus

Q R = \frac{2 \sin (108^{\circ})}{\sin (24^{\circ})}

Therefore:

P R = P Q + Q R = \frac{1}{\tan (24^{\circ})} + \frac{2 \sin (108^{\circ})}{\sin (24^{\circ})} \approx 6.92

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