Question:
A and B are two points on one bank of a straight river and C, D are two other points on the other bank... AB=a, $\angle CAD=α, \angle DAB=β, \angle CBA=γ$, then CD is equal to
A and B are two points on one bank of a straight river and C, D are two other points on the other bank... AB=a, $\angle CAD=α, \angle DAB=β, \angle CBA=γ$, then CD is equal to
Show Hint
A and B are two points on one bank of a straight river and C, D are two other points on the other bank... AB=a, $\angle CAD=α, \angle DAB=β, \angle CBA=γ$, then CD is equal to
Updated On: Apr 15, 2026
- $\frac{a \sin \beta \cdot \sin \gamma}{\sin \alpha \cdot \sin(\alpha+\beta+\gamma)}$
- $\frac{a \sin \alpha \cdot \sin \gamma}{\sin \beta \cdot \sin(\alpha+\beta+\gamma)}$
- $\frac{a \sin \alpha \cdot \sin \beta}{\sin \gamma \cdot \sin(\alpha+\beta+\gamma)}$
- None of the above
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
Apply the Sine Rule in triangles $\Delta CAB$ and $\Delta CAD$.
Step 2: Analysis
In $\Delta CAB$, $\frac{AC}{\sin \gamma} = \frac{a}{\sin(\alpha+\beta+\gamma)}$, so $AC = \frac{a \sin \gamma}{\sin(\alpha+\beta+\gamma)}$.
Step 3: Evaluation
In $\Delta CAD$, $\frac{CD}{\sin \alpha} = \frac{AC}{\sin \beta}$.
Step 4: Conclusion
Substituting $AC$, we get $CD = \frac{a \sin \alpha \cdot \sin \gamma}{\sin \beta \cdot \sin(\alpha+\beta+\gamma)}$.
Final Answer: (b)
Apply the Sine Rule in triangles $\Delta CAB$ and $\Delta CAD$.
Step 2: Analysis
In $\Delta CAB$, $\frac{AC}{\sin \gamma} = \frac{a}{\sin(\alpha+\beta+\gamma)}$, so $AC = \frac{a \sin \gamma}{\sin(\alpha+\beta+\gamma)}$.
Step 3: Evaluation
In $\Delta CAD$, $\frac{CD}{\sin \alpha} = \frac{AC}{\sin \beta}$.
Step 4: Conclusion
Substituting $AC$, we get $CD = \frac{a \sin \alpha \cdot \sin \gamma}{\sin \beta \cdot \sin(\alpha+\beta+\gamma)}$.
Final Answer: (b)
Was this answer helpful?
0
0
Top MET Mathematics Questions
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- The equation $3^{3x + 4} = 9^{2x - 2},\ x>0$ has the solution
- A parallelogram is constructed on the vectors $\mathbf{a} = 3\alpha - \beta$, $\mathbf{b} = \alpha + 3\beta$. If $|\alpha| = |\beta| = 2$ and the angle between $\alpha$ and $\beta$ is $\dfrac{\pi}{3}$, then the length of a diagonal of the parallelogram is
- Every group of order 7 is
- Let $U_{n} = 2 + 2^{3} + 2^{5} + \cdots + 2^{2n+1}$ and $V_{n} = 1 + 4 + 4^{2} + \cdots + 4^{n-1}$. Then $\displaystyle\lim_{n \to \infty} \dfrac{U_n}{V_n}$ is equal to
View More Questions
Top MET Geometry Questions
- In a \( \Delta ABC \), \( \angle B = 90^\circ \), then \( \tan^2\left(\frac{A}{2}\right) \) is
- In a triangle, if $r₁ > r₂ > r₃$ then
- If $t₁, t₂$ and $t₃$ are distinct, the points $(t₁, 2at₁+at₁³), (t₂, 2at₂+at₂³), (t₃, 2at₃+at₃³)$ are collinear if
- If the lines $a₁x+b₁y+c₁=0$, $a₁x+b₁y+c₂=0$, $a₂x+b₂y+d₁=0$ and $a₂x+b₂y+d₂=0$ are sides of a rhombus, then
- Total number of regions in which 'n' coplanar lines can divide the plane, it is known that no two lines are parallel and no three of them are concurrent, is equal to
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions