(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 $\tan 15^{\circ}+\frac{1}{\tan 75^{\circ}}+\frac{1}{\tan 105^{\circ}}+\tan 195^{\circ}=2a$,then the value of $\left(a+\frac{1}{a}\right)$ is:

DifficultJEE MAIN 2023

View Solution

If $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7} = \frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}$,then $\sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \frac{11 \pi}{14} \sin \frac{13 \pi}{14} = $

MediumTS EAMCET 2023

View Solution

If $a \cos \theta + b \sin \theta = m$ and $a \sin \theta - b \cos \theta = n,$ then ${a^2} + {b^2} = $

Easy

View Solution

If $\sin A+\sin B=\sqrt{3}(\cos B-\cos A)$,then $\sin 3A+\sin 3B$ is equal to

DifficultAP EAMCET 2007

View Solution

The value of $\sin\,10^o \sin\,30^o \sin\,50^o \sin\,70^o$ is

DifficultJEE MAIN 2019

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 $\tan 15^{\circ}+\frac{1}{\tan 75^{\circ}}+\frac{1}{\tan 105^{\circ}}+\tan 195^{\circ}=2a$,then the value of $\left(a+\frac{1}{a}\right)$ is:

If $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7} = \frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}$,then $\sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \frac{11 \pi}{14} \sin \frac{13 \pi}{14} = $

If $a \cos \theta + b \sin \theta = m$ and $a \sin \theta - b \cos \theta = n,$ then ${a^2} + {b^2} = $

If $\sin A+\sin B=\sqrt{3}(\cos B-\cos A)$,then $\sin 3A+\sin 3B$ is equal to

The value of $\sin\,10^o \sin\,30^o \sin\,50^o \sin\,70^o$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module