The sides of a triangle are sin theta, cos th | vedclass

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

Question

(B) Let the sides be $a = \sin 	heta$,$b = \cos 	heta$,and $c = \sqrt{1 + \sin 	heta \cos 	heta}$.Since $0 < 	heta < \frac{\pi}{2}$,both $\sin

Vedclass · Accepted Answer

$\frac{2 \pi}{3}$

Vedclass · Answer

(B) Let the sides be $a = \sin 	heta$,$b = \cos 	heta$,and $c = \sqrt{1 + \sin 	heta \cos 	heta}$.Since $0 Comparing the squares of the sides: $a^2 = \sin^2 	heta$,$b^2 = \cos^2 	heta$,and $c^2 = 1 + \sin 	heta \cos 	heta$.Since $c^2 = \sin^2 	heta + \cos^2 	heta + \sin 	heta \cos 	heta$,it is clear that $c^2 > a^2$ and $c^2 > b^2$,so $c$ is the longest side.The greatest angle $C$ is opposite to side $c$.Using the Law of Cosines: $\cos C = \frac{a^2 + b^2 - c^2}{2ab}$.$\cos C = \frac{\sin^2 	heta + \cos^2 	heta - (1 + \sin 	heta \cos 	heta)}{2 \sin 	heta \cos 	heta}$.$\cos C = \frac{1 - 1 - \sin 	heta \cos 	heta}{2 \sin 	heta \cos 	heta} = \frac{-\sin 	heta \cos 	heta}{2 \sin 	heta \cos 	heta} = -\frac{1}{2}$.Since $\cos C = -\frac{1}{2}$,$C = 120^{\circ} = \frac{2 \pi}{3}$.

The sides of a triangle are $\sin \theta, \cos \theta$ and $\sqrt{1 + \sin \theta \cos \theta}$ for some $0 < \theta < \frac{\pi}{2}$. Then the greatest angle of the triangle is:

Similar Questions

The circumradius $R$ of an isosceles triangle $ABC$ is four times its inradius $r$. If $A = B$,then which of the following is true?

In $\triangle ABC$,we are given that $3 \sin A + 4 \cos B = 6$ and $4 \sin B + 3 \cos A = 1$. Then,the measure of $\angle C$ is $....^{\circ}$

In $\triangle ABC$,if $\cos A + \cos C = 4 \sin^2 \frac{B}{2}$,then the ratio between the perimeter of the triangle and $(a+c)$ is

In a triangle $ABC$,if $a < b < c$ and $\frac{a^3+b^3+c^3}{\sin^3 A+\sin^3 B+\sin^3 C}=8$,then the maximum value of $c$ is

Let $S=\{\theta \in[0,2 \pi): \tan (\pi \cos \theta)+\tan (\pi \sin \theta)=0\}$. Then $\sum_{\theta \in S } \sin ^2\left(\theta+\frac{\pi}{4}\right)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module