(D) Let the intersection point of the two roads be $A$. Let the position of the bus be $B$ and the position of the car be $C$.Given that $AB = 2 \, km

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

(D) Let the intersection point of the two roads be $A$. Let the position of the bus be $B$ and the position of the car be $C$.Given that $AB = 2 \, km$,$AC = 3 \, km$,and the angle $\angle BAC = 60^o$.Using the Law of Cosines in $\triangle ABC$:$BC^2 = AB^2 + AC^2 - 2(AB)(AC) \cos(60^o)$$BC^2 = 2^2 + 3^2 - 2(2)(3) \left(\frac{1}{2}\right)$$BC^2 = 4 + 9 - 6$$BC^2 = 7$$BC = \sqrt{7} \, km$.Thus,the direct distance between the two vehicles is $\sqrt{7} \, km$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Mix Examples-Trigonometrical Ratios, Functions and Identities

Easy

Two straight roads intersect at an angle of $60^o$. $A$ bus on one road is $2 \, km$ away from the intersection and a car on the other road is $3 \, km$ away from the intersection. Then the direct distance between the two vehicles is

A
$1 \, km$
B
$\sqrt{2} \, km$
C
$4 \, km$
D
$\sqrt{7} \, km$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Ratios, Functions and Identities

Subtopic

Mix Examples-Trigonometrical Ratios, Functions and Identities

If $\frac{1}{\sin 45^{\circ} \sin 46^{\circ}}+\frac{1}{\sin 46^{\circ} \sin 47^{\circ}}+\ldots$ up to $45$ terms $=\frac{1}{\sin x^{\circ}}$,then $\sin \left(\frac{\pi}{2} x\right)=$

DifficultTS EAMCET 2022

View Solution

$\frac{\sin 1^{\circ}+\sin 2^{\circ}+\ldots+\sin 89^{\circ}}{2(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{\circ})+1} = $

DifficultAP EAMCET 2024

View Solution

Prove that $\cot x \cot 2x - \cot 2x \cot 3x - \cot 3x \cot x = 1$.

Medium

View Solution

If $x$ and $y$ are acute angles such that $\cos x + \cos y = \frac{3}{2}$ and $\sin x + \sin y = \frac{3}{4}$,then $\sin(x + y)$ equals to

DifficultTS EAMCET 2014

View Solution

Evaluate: $\sin 6^{\circ} + \sin 54^{\circ} + \sin 126^{\circ} + \cos 156^{\circ}$

EasyTS EAMCET 2023

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

Two straight roads intersect at an angle of $60^o$. $A$ bus on one road is $2 \, km$ away from the intersection and a car on the other road is $3 \, km$ away from the intersection. Then the direct distance between the two vehicles is

Similar Questions

If $\frac{1}{\sin 45^{\circ} \sin 46^{\circ}}+\frac{1}{\sin 46^{\circ} \sin 47^{\circ}}+\ldots$ up to $45$ terms $=\frac{1}{\sin x^{\circ}}$,then $\sin \left(\frac{\pi}{2} x\right)=$

$\frac{\sin 1^{\circ}+\sin 2^{\circ}+\ldots+\sin 89^{\circ}}{2(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{\circ})+1} = $

Prove that $\cot x \cot 2x - \cot 2x \cot 3x - \cot 3x \cot x = 1$.

If $x$ and $y$ are acute angles such that $\cos x + \cos y = \frac{3}{2}$ and $\sin x + \sin y = \frac{3}{4}$,then $\sin(x + y)$ equals to

Evaluate: $\sin 6^{\circ} + \sin 54^{\circ} + \sin 126^{\circ} + \cos 156^{\circ}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module