(C) In a $\triangle ABC$,it is given that $a=1$,$b=\sqrt{3}$ and $\angle C=\frac{\pi}{6}$.Using the Law of Cosines:$\cos C = \frac{a^2 + b^2 - c^2}{2a

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) In a $\triangle ABC$,it is given that $a=1$,$b=\sqrt{3}$ and $\angle C=\frac{\pi}{6}$.Using the Law of Cosines:$\cos C = \frac{a^2 + b^2 - c^2}{2ab}$$\cos \frac{\pi}{6} = \frac{1^2 + (\sqrt{3})^2 - c^2}{2(1)(\sqrt{3})}$$\frac{\sqrt{3}}{2} = \frac{1 + 3 - c^2}{2\sqrt{3}}$$\frac{\sqrt{3}}{2} = \frac{4 - c^2}{2\sqrt{3}}$Multiply both sides by $2\sqrt{3}$:$3 = 4 - c^2$$c^2 = 4 - 3 = 1$Since $c$ represents the length of a side,$c = 1$.Therefore,option $C$ is correct.

Class 11 Mathematics Trigonometrical Equations Relation between sides and angles, Solutions of triangles

Easy

In a $\triangle ABC$,$a=1$,$b=\sqrt{3}$ and $\angle C=\pi/6$. Then the measure of the third side $c=$

AP EAMCET 2020 All AP EAMCET

A
$4$
B
$3$
C
$1$
D
$2$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Equations

Subtopic

Relation between sides and angles, Solutions of triangles

Previous Year

AP EAMCET 2020 Paper All AP EAMCET years →

In $\triangle ABC$,find the value of $\frac{\sin 2A + \sin 2B + \sin 2C}{\cos A + \cos B + \cos C - 1}$.

EasyAP EAMCET 2023

View Solution

Angles of a triangle are in the ratio $4:1:1$. Then the ratio of its greatest side to its perimeter is

EasyMHT CET 2023

View Solution

Two sides of a triangle are given by the roots of the equation $x^2-5x+6=0$ and the angle between the sides is $\frac{\pi}{3}$. Then,the perimeter of the triangle is

EasyTS EAMCET 2005

View Solution

With usual notations,the perimeter of a triangle $ABC$ is $6$ times the arithmetic mean of the sines of its angles. If $a=1$,then the measure of angle $A$ is:

MediumMHT CET 2021

View Solution

With usual notation in a $\Delta ABC$,if $R = k \frac{(r_1 + r_2)(r_2 + r_3)(r_3 + r_1)}{r_1 r_2 + r_2 r_3 + r_3 r_1}$,where $k$ has the value equal to:

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

In a $\triangle ABC$,$a=1$,$b=\sqrt{3}$ and $\angle C=\pi/6$. Then the measure of the third side $c=$

Similar Questions

In $\triangle ABC$,find the value of $\frac{\sin 2A + \sin 2B + \sin 2C}{\cos A + \cos B + \cos C - 1}$.

Angles of a triangle are in the ratio $4:1:1$. Then the ratio of its greatest side to its perimeter is

Two sides of a triangle are given by the roots of the equation $x^2-5x+6=0$ and the angle between the sides is $\frac{\pi}{3}$. Then,the perimeter of the triangle is

With usual notations,the perimeter of a triangle $ABC$ is $6$ times the arithmetic mean of the sines of its angles. If $a=1$,then the measure of angle $A$ is:

With usual notation in a $\Delta ABC$,if $R = k \frac{(r_1 + r_2)(r_2 + r_3)(r_3 + r_1)}{r_1 r_2 + r_2 r_3 + r_3 r_1}$,where $k$ has the value equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module