Question:
In triangle ABC, with usual notations, if \(a = 4,b = 5\) and \(c = 6\), then angle C is equal to...
In triangle ABC, with usual notations, if \(a = 4,b = 5\) and \(c = 6\), then angle C is equal to...
Show Hint
Find cos A and cos C by the cosine rule and compare cos 2A with cos C.
Updated On: Oct 1, 2026
- \(A\)
- \(2A\)
- \(3A\)
- \(\frac{A}{2}\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Cosine of C
\(\cos C = \frac{a^2+b^2-c^2}{2ab} = \frac{16+25-36}{40} = \frac18\).
Step 2: Cosine of A
\(\cos A = \frac{b^2+c^2-a^2}{2bc} = \frac{25+36-16}{60} = \frac34\).
Step 3: Double angle
\(\cos2A = 2\cos^2A - 1 = 2\cdot\frac{9}{16} - 1 = \frac18\).
Step 4: Compare
\(\cos2A = \cos C\) and both angles lie in the range where cosine is one-to-one, so \(C = 2A\). Option (B).
Final Answer:
Angle C equals 2A. \[ \boxed{\text{(B)}\ C = 2A} \]
\(\cos C = \frac{a^2+b^2-c^2}{2ab} = \frac{16+25-36}{40} = \frac18\).
Step 2: Cosine of A
\(\cos A = \frac{b^2+c^2-a^2}{2bc} = \frac{25+36-16}{60} = \frac34\).
Step 3: Double angle
\(\cos2A = 2\cos^2A - 1 = 2\cdot\frac{9}{16} - 1 = \frac18\).
Step 4: Compare
\(\cos2A = \cos C\) and both angles lie in the range where cosine is one-to-one, so \(C = 2A\). Option (B).
Final Answer:
Angle C equals 2A. \[ \boxed{\text{(B)}\ C = 2A} \]
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Trigonometric Functions Questions
- The number of principal solutions of $\tan 2 \theta = 1$ is
- In $\Delta ABC \left(a-b\right)^{2} cos^{2} \frac{C}{2} + \left(a+b\right)^{2} sin^{2} \frac{C}{2} = $
- Find the equation of tangent of at
The number of solutions of tanx+secx=2cosx, n(0,2π) are?
What is the number of solutions of tanx + secx = 2 cosx if x belongs to (0, 2π)?
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions