angles are equal. Find the
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We have an angle AOB with a measure of 40°. Point P is inside this angle, and from P, two lines are drawn perpendicular to OA and OB, meeting OA at M and OB at N, respectively. Show more…
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Two triangles, RPQ and NQP, are placed together to create a parallelogram as shown below. Triangles RPQ and NQP are connected at side PQ. Angle R is 60 degrees, angle RPQ is 80 degrees, angle NQP is 80 degrees, and angle QPN is 40 degrees. What is the measure of angle PQR? What is the measure of angle QNP?
Dr Harish V.
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Jason J.
In triangle $P Q R$ shown in Fig. 12.14, find the lengths of $P Q$ and $P R$. $\tan 38^{\circ}=\frac{P Q}{Q R}=\frac{P Q}{7.5}$ hence $\quad P Q=7.5 \tan 38^{\circ}=7.5(0.7813)$ $=5.860 \mathrm{~cm}$ $\cos 38^{\circ}=\frac{Q R}{P R}=\frac{7.5}{P R}$ hence $\quad P R=\frac{7.5}{\cos 38^{\circ}}=\frac{7.5}{0.7880}=9.518 \mathrm{~cm}$
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