Question : If $\triangle$PQR is right-angled at Q, PQ = 12 cm and $\angle$PRQ = 30°, then what is the value of QR?
Option 1: $12\sqrt{3}$
Option 2: $12\sqrt2$
Option 3: $12$
Option 4: $24$
Correct Answer: $12\sqrt{3}$
Solution : $\triangle$ PQR is a right-angled at Q. So, Hypotenuse is PR. We know, tan $x$ = $\frac{\text{Opposite Side}}{\text{Adjacent Side}}$ tan($\angle$PRQ) = $\frac{PQ}{QR}$ ⇒ tan 30° = $\frac{12}{QR}$ ⇒ $\frac{1}{\sqrt{3}} = \frac{12}{QR}$ $\therefore$ QR = $12\sqrt{3}$ cm Hence, the correct answer is $12\sqrt{3}$.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : In $\triangle$PQR, $\angle$ PQR = $90^{\circ}$, PQ = 5 cm and QR = 12 cm. What is the radius (in cm) of the circumcircle of $\triangle$PQR?
Question : In a $\triangle P Q R, \angle P: \angle Q: \angle R=3: 4: 8$. The shortest side and the longest side of the triangle, respectively, are:
Question : $\triangle$ PQR circumscribes a circle with centre O and radius r cm such that $\angle$ PQR = $90^{\circ}$. If PQ = 3 cm, QR = 4 cm, then the value of r is:
Question : In a $\triangle \mathrm{PQR}$ and $\triangle\mathrm{ABC}$, $\angle$P = $\angle$A and AC = PR. Which of the following conditions is true for $\triangle$PQR and $\triangle$ABC to be congruent?
Question : $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are two triangles such that $\triangle \mathrm{ABC} \cong \triangle \mathrm{FDE}$. If AB = 5 cm, $\angle$B = 40° and $\angle$A = 80°, then which of the following options is true?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile