MHT CET · Maths · Properties of Triangles
In a triangle \(\mathrm{ABC}\), with usual notations, if \(\mathrm{m} \angle \mathrm{A}=60^{\circ}, \mathrm{b}=8, \mathrm{a}=6\) and \(\mathrm{B}=\sin ^{-1} x\), then \(x\) has the value
- A \(\frac{\sqrt{3}}{2}\)
- B \(\frac{2}{\sqrt{3}}\)
- C \(2 \sqrt{3}\)
- D \(\frac{1}{2 \sqrt{3}}\)
Answer & Solution
Correct Answer
(B) \(\frac{2}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
By sine rule, we get
\(
\begin{aligned}
& \frac{\sin \mathrm{A}}{\mathrm{a}}=\frac{\sin \mathrm{B}}{\mathrm{b}} \\
& \Rightarrow \frac{\sin 60^{\circ}}{6}=\frac{x}{8} \\
& \Rightarrow x=\frac{\sqrt{3}}{2} \times \frac{8}{6} \\
& \Rightarrow x=\frac{2}{\sqrt{3}}
\end{aligned}
\)
\(
\begin{aligned}
& \frac{\sin \mathrm{A}}{\mathrm{a}}=\frac{\sin \mathrm{B}}{\mathrm{b}} \\
& \Rightarrow \frac{\sin 60^{\circ}}{6}=\frac{x}{8} \\
& \Rightarrow x=\frac{\sqrt{3}}{2} \times \frac{8}{6} \\
& \Rightarrow x=\frac{2}{\sqrt{3}}
\end{aligned}
\)
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
- The combined equation of the lines passing through the origin making an acute angle \(\propto\) with the line \(y=x\) isMHT CET 2022 Easy
- If \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) are mutually perpendicular vectors having magnitudes \(1,2,3\) respectively, then the value of \(\left[\begin{array}{lll}\bar{a}+\bar{b}+\bar{c} & \bar{b}-\bar{a} & \bar{c}\end{array}\right]\) isMHT CET 2024 Medium
- Mean and variance of six observations are 6 and 12 respectively. If each observation is multiplied by 3 , then new variance of the resulting observations isMHT CET 2024 Medium
- The value of \(\sin \left[\tan ^{-1}\left(\frac{1-x^2}{2 x}\right)+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right]\) isMHT CET 2025 Medium
- The region represented by the inequation system \(x, y \geq 0, y \leq 6, x+y \leq 3\), isMHT CET 2008 Easy
- If \(x^k+y^k=a^k(a, k>0)\) and \(\frac{d y}{d x}+\left(\frac{y}{x}\right)^{\frac{1}{b}}-0\), then \(\mathrm{k}\) has the valueMHT CET 2023 Medium
More PYQs from MHT CET
- A random variable \(X\) has following p.d.f.
\(\mathrm{f}(\mathrm{x})=\mathrm{k} x(1-x), 0 \leqslant x \leqslant 1\)
and \(\mathrm{P}(x>a)=\frac{20}{27}\), then \(a=\)MHT CET 2025 Medium - The ionic charges on chromate ion and dichromate ion respectively isMHT CET 2019 Easy
- Exponential growth equation is\(N _{ t }= N _0 e ^{ rt }\) where \(N _{ t }\), population density after time t then what does \(N _{ 0 }\) and r refers to respectivelyMHT CET 2020 Hard
- The rate for reaction \(\mathrm{A}+\mathrm{B} \rightarrow\) product, is \(1.8 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\). Calculate the rate constant if the reaction is second order in \(\mathrm{A}\) and first order in \(\mathrm{B} .([\mathrm{A}]=0.2 \mathrm{M} ;[\mathrm{B}]=0.1 \mathrm{M})\)MHT CET 2023 Medium
- Which of the following acids does not contain -COOH group?MHT CET 2012 Hard
- Two cells \(\mathrm{E}_1\) and \(\mathrm{E}_2\) having equal \(\mathrm{EMF}\) ' \(\mathrm{E}\) ' and internal resistances \(r_1\) and \(r_2\left(r_1>r_2\right)\) respectively are connected in series. This combination is connected to an external resistance ' \(R\) '. It is observed that the potential difference across the cell \(E_1\) becomes zero. The value of ' \(R\) ' will beMHT CET 2023 Medium