MHT CET · Maths · Properties of Triangles
With usual notations, if the angles \(A, B, C\) of a \(\triangle A B C\) are in A.P. and \(b: c=\sqrt{3}: \sqrt{2}\),
then \(\angle \mathrm{A}=\)
- A \(55^{\circ}\)
- B \(45^{\circ}\)
- C \(35^{\circ}\)
- D \(75^{\circ}\)
Answer & Solution
Correct Answer
(D) \(75^{\circ}\)
Step-by-step Solution
Detailed explanation
(B)
Since \(A, B, C\) are in A.P., \(2 B=A+C \Rightarrow B=60^{\circ}\)
We know that, \(\frac{\sin B}{b}=\frac{\sin C}{c} \Rightarrow \sin C=\frac{C}{b} \times \sin 60^{\circ}\)
\(\therefore \sin C=\frac{\sqrt{2}}{\sqrt{3}} \times \frac{\sqrt{3}}{2}=\frac{1}{\sqrt{2}}\)
\(\therefore \quad C=45^{\circ} \Rightarrow A=180^{\circ}-\left(60^{\circ}+45^{\circ}\right)=75^{\circ}\)
Since \(A, B, C\) are in A.P., \(2 B=A+C \Rightarrow B=60^{\circ}\)
We know that, \(\frac{\sin B}{b}=\frac{\sin C}{c} \Rightarrow \sin C=\frac{C}{b} \times \sin 60^{\circ}\)
\(\therefore \sin C=\frac{\sqrt{2}}{\sqrt{3}} \times \frac{\sqrt{3}}{2}=\frac{1}{\sqrt{2}}\)
\(\therefore \quad C=45^{\circ} \Rightarrow A=180^{\circ}-\left(60^{\circ}+45^{\circ}\right)=75^{\circ}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If the mean and S.D. of the data \(3,5,7, \mathrm{a}, \mathrm{b}\) are 5 and 2 respectively, then \(\mathrm{a}\) and \(\mathrm{b}\) are the roots of the equationMHT CET 2023 Easy
- If \(f(x)=\frac{e^{x^2}-\cos x}{x^2}\) if \(x \neq 0\) is continuous at \(x=0\), then \(f(0)=\).MHT CET 2022 Medium
- If \(x=\sin \theta, y=\sin ^3 \theta\), then \(\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}\) at \(\theta=\frac{\pi}{2}\) isMHT CET 2024 Easy
- If \(\mathrm{A}=\left[\begin{array}{cc}5 a & -\mathrm{b} \\ 3 & 2\end{array}\right]\) and A.adj \(\mathrm{A}=\mathrm{AA}^{\mathrm{T}}\), then \(5 a+\mathrm{b}=\)MHT CET 2025 Medium
- If the scalar triple product of the vectors and is 272 then …MHT CET 2019 Easy
- The inverse of statement pattern \((p \vee q) \rightarrow(p \wedge q)\) isMHT CET 2022 Easy
More PYQs from MHT CET
- A sonometer wire is stretched by hanging a metal bob, the fundamental frequency of the wire is ' \(n_1\) '. When the bob is completely immersed in water, the frequency of vibration of wire becomes ' \(\mathrm{n}_2\) '. The relative density of the metal of the bob isMHT CET 2024 Hard
- If \(n(X)=700, n(A)=200, n(B)=300,\) \(n(A \cap B)=100\), where \(X\) is universal set and \(A\) and \(\mathrm{B}\) are subsets of \(\mathrm{X}\), then \(\mathrm{n}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)=\)MHT CET 2020 Medium
- The last column in the truth table of the statement pattern \([p \rightarrow(q \wedge \sim p)] \vee[(p \vee \sim q) \wedge p]\) isMHT CET 2025 Easy
- The equation \(12 x^{2}+7 x y+a y^{2}+13 x-y+3=0\)
represents a pair of perpendicular lines. Then the value of ' \(a\) ' isMHT CET 2008 Easy - What is effective atomic number of cobalt in \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}\) if \(\operatorname{Co}(Z=27) ?\)MHT CET 2021 Medium
- Identify the alkyne formed by reaction of calcium carbide with water?MHT CET 2025 Easy