Question : In $\triangle P Q R$, $\angle Q=90^{\circ}$, $PQ=8$ cm and $\angle P R Q=45^{\circ}$ Find the length of $QR$.
Option 1: 6 cm
Option 2: 3 cm
Option 3: 5 cm
Option 4: 8 cm
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Correct Answer: 8 cm
Solution : Putting all the given values, we get, $\angle PQR +\angle PRQ + \angle RPQ = 180°$ $90° + 45°+\angle RPQ = 180°$ $\therefore \angle RPQ= 45°$ ⇒ PQR is an isosceles triangle. $\therefore$ PQ = QR = 8 cm Hence, the correct answer is 8 cm.
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Question : $\triangle PQR$ is right-angled at $Q$. The length of $PQ$ is 5 cm and $\angle P R Q=30^{\circ}$. Determine the length of the side $QR$.
Question : If $\triangle \mathrm{ABC} \cong \triangle \mathrm{PQR}, \mathrm{BC}=6 \mathrm{~cm}$, and $\angle \mathrm{A}=75^{\circ}$, then which one of the following is true?
Question : $\triangle ABC$ and $\triangle PQR$ are two triangles. AB = PQ = 6 cm, BC = QR =10 cm, and AC = PR = 8 cm. If $\angle ABC = x$, then what is the value of $\angle PRQ$?
Question : In a triangle PQR, $\angle$Q = 90°. If PQ = 12 cm and QR = 5 cm, then what is the radius (in cm) of the circumcircle of the triangle?
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