(C) Let the sides of the triangle be $a = 3$, $b = 5$, and $c = 7$.The largest angle is opposite the longest side, which is $c = 7$. Let this angle be

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

(C) Let the sides of the triangle be $a = 3$, $b = 5$, and $c = 7$.The largest angle is opposite the longest side, which is $c = 7$. Let this angle be $C$.Using the Law of Cosines: $\cos C = \frac{a^2 + b^2 - c^2}{2ab}$.Substitute the values: $\cos C = \frac{3^2 + 5^2 - 7^2}{2(3)(5)}$.$\cos C = \frac{9 + 25 - 49}{30} = \frac{34 - 49}{30} = \frac{-15}{30} = -\frac{1}{2}$.Since $\cos C = -\frac{1}{2}$, the angle $C = \arccos(-\frac{1}{2}) = \frac{2\pi}{3}$.

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

Difficult

With the usual notations, if the lengths of the sides of a triangle are $3 \text{ units}$, $5 \text{ units}$, and $7 \text{ units}$, then the largest angle of the triangle is

MHT CET 2026 All MHT CET

A
$\frac{\pi}{2}$
B
$\frac{\pi}{3}$
C
$\frac{2\pi}{3}$
D
$\frac{\pi}{4}$

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

MHT CET 2026 Paper All MHT CET years →

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one,then the sides of the triangle (in units) are

EasyMHT CET 2023

View Solution

If in $\triangle ABC$,with usual notations,the angles are in $A$.$P$.,then $\frac{a}{c} \sin 2C + \frac{c}{a} \sin 2A =$

MediumMHT CET 2021

View Solution

If,in a $\triangle ABC$,$\tan \frac{A}{2} = \frac{5}{6}$ and $\tan \frac{C}{2} = \frac{2}{5}$,then $a, b, c$ are such that :

DifficultAP EAMCET 2006

View Solution

We are given $b, c$ and $\sin B$ such that $B$ is acute and $b < c \sin B$. Then

Easy

View Solution

In a triangle $ABC$,with usual notations,if $a=5$,$b=7$,and $\sin A=\frac{3}{4}$,then the total number of triangles possible is:

MediumMHT CET 2025

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

With the usual notations, if the lengths of the sides of a triangle are $3 \text{ units}$, $5 \text{ units}$, and $7 \text{ units}$, then the largest angle of the triangle is

Similar Questions

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one,then the sides of the triangle (in units) are

If in $\triangle ABC$,with usual notations,the angles are in $A$.$P$.,then $\frac{a}{c} \sin 2C + \frac{c}{a} \sin 2A =$

If,in a $\triangle ABC$,$\tan \frac{A}{2} = \frac{5}{6}$ and $\tan \frac{C}{2} = \frac{2}{5}$,then $a, b, c$ are such that :

We are given $b, c$ and $\sin B$ such that $B$ is acute and $b < c \sin B$. Then

In a triangle $ABC$,with usual notations,if $a=5$,$b=7$,and $\sin A=\frac{3}{4}$,then the total number of triangles possible is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module