MHT CET · Maths · Properties of Triangles
If two sides of a triangle are \(\sqrt{3}-2\) and \(\sqrt{3}+2\) units and their included angle is \(60^{\circ}\), then the third side of the triangle is
- A 15 units
- B \(\sqrt{15}-2\) units
- C \(\sqrt{15}+2\) units
- D \(\sqrt{15}\) units
Answer & Solution
Correct Answer
(D) \(\sqrt{15}\) units
Step-by-step Solution
Detailed explanation
\(c^2 = a^2 + b^2 - 2ab \cos C\) \(c^2 = (\sqrt{3}-2)^2 + (\sqrt{3}+2)^2 - 2(\sqrt{3}-2)(\sqrt{3}+2) \cos 60^{\circ}\)
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
- The perpendicular distance between the lines given by \((x-2 \mathrm{y}+1)^2+\mathrm{k}(x-2 \mathrm{y}+1)=0\) is \(\sqrt{5}\), then \(\mathrm{k}=\)MHT CET 2025 Medium
- The domain of the function \(\mathrm{f}(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^2}}\) isMHT CET 2024 Easy
- The differential equation of all parabolas whose axis is isMHT CET 2017 Medium
- In a triangle ABC , with usual notations, \(\frac{\cos B+\cos C}{b+c}+\frac{\cos A}{a}\) has the valueMHT CET 2024 Hard
- Let \(\alpha(a)\) and \(\beta(a)\) be the roots of the equation \((\sqrt[3]{1+a}-1) x^2+(\sqrt{1+a}-1) x+(\sqrt[6]{1+a}-1)=0\) where \(a\gt-1\) then \(\lim _{a \rightarrow 0^{+}} \alpha(a)\) and \(\lim _{a \rightarrow 0^{+}} \beta(a)\) respectively areMHT CET 2024 Medium
- MHT CET 2019 Medium
More PYQs from MHT CET
- A water drop of \(0.01 \mathrm{~cm}^3\) is squeezed between two glass plates and spreads in to area of \(10 \mathrm{~cm}^2\). If surface tension of water is 70 dyne \(/ \mathrm{cm}\) then the normal force required to separate glass plates from each other will beMHT CET 2025 Medium
- \(\int \cot x \cdot \log [\log (\sin x)] d x=\)MHT CET 2020 Hard
- What is the oxidation number of Mn in \(\mathrm{MnO}_4^{-}\)?MHT CET 2024 Medium
- When the observer moves towards the stationary source with velocity \(V_1\), the apparent frequency of the emitted note is \(F_1\). When the observer moves away from the source with velocity \(V_1\), the apparent frequency is \(F_2\). If \(V\) is the velocity of sound in air and \(\frac{F_1}{F_2}=2\) then \(\frac{V}{V_1}=\) ?MHT CET 2016 Medium
- The internal energy of a monoatomic ideal gas molecule isMHT CET 2023 Easy
- \(\int_{-2}^{1}[x+1] d x=\)
(Where \([x]\) is greatest integer function not greater than \(x\) )MHT CET 2020 Hard