Question

PQRS is a Quadrilateral such that pq=8cm , QR = 4cm and SR=5cm If PQ and SR are Produced to meet at x such that Qx = 8cm. and RX=10cm Calculate Ps to a suitable degree of accuracy ​

Answer 1

PS ≈ 6.08

Explanation:

All of the side lengths are given except PS. It can be found using the Law of Cosines, twice.

The first use of the Law of Cosines will be to find the cosine of the angle at X.

QR² = QX² +RX² -2(QX)(RX)cos(X)

cos(X) = (QX² +RX² -QR²)/(2·QX·RX) = (8² +10² -4²)/(2·8·10) = 37/40

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Now, the Law of Cosines can be used to find PS:

PS² = PX² +SX² -2(PX)(SX)cos(X)

PS² = 16² +15² -2(16)(15)(37/40) = 37

PS = √37 ≈ 6.083

The length of PS is about 6.08 units.

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As the attachment shows, the problem can also be solved using a geometry app to draw the figure and make the measurement.