Home
Class 12
MATHS
The straight roads intersect at an angle...

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

A

1 km

B

`sqrt2` km

C

4 km

D

`sqrt7` km

Text Solution

AI Generated Solution

To find the direct distance between the bus and the car, we can use the cosine rule in the triangle formed by the bus, car, and the intersection point of the roads. Here’s a step-by-step solution: ### Step 1: Understand the Geometry We have two roads intersecting at point A, forming an angle of 60°. The bus is located at point B, which is 2 km away from A, and the car is located at point C, which is 3 km away from A. ### Step 2: Label the Distances - Distance AB (bus to intersection) = 2 km - Distance AC (car to intersection) = 3 km ...
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|95 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise SOLVED MCQ|2 Videos

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|31 Videos

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

Similar Questions

Explore conceptually related problems

Two cars A and B are moving west to east and south to north, respectively, along crossroads. A moves with a speed of 20 m s^-1 and is 500 m away from the point of intersection of cross roads and B moves with a speed of 15 ms^-1 and is 400 m away from the point of intersection of cross roads. Find the shortest distance between them.

Two boats leave a place at the same time. One travels 56 km in the direction N 40^@ E, while the other travels 48 km in the direction S 80^@ E. What is the distance between the boats?

Two highways are perpendicular to each other imagine them to be along the x-axis and the y-axis, respectively. At the instant t = 0, a police car P is at a distance d = 400 m from the intersection and moving at speed of 8 km//h towards it at a speed of 60 km//h along they y-axis. The minimum distance between the cars is

Two lines passing through the point (2,3) intersect each other at an angle 60^0 . If slope of one line is 2, find the equation of the other line.

Two lines passing through the point (2, 3) intersects each other at an angle of 60^o . If slope of one line is 2, find equation of the other line.

A fire in a building B is reported on telephone to two fire stations P and Q , 20km apart from each other on a straight road. P observes that the fire is at an angle of 60o to the road and Q observes that it is at an angle of 45o to the road. Which station should send its team and how much will this team have to travel?

P is a point on either of the two lines y - sqrt3|x|=2 at a distance 5 units from their point of intersection The coordinates of the foot of the perpendicular from P on the bisector of the angle between them are

P is a point equidistant from two lines l and m intersecting at a point A , Show that A P bisects the angle between them.

A straight road is at a distance of 5sqrt(2) km from a place. The shortest distance of the road from the place is in the N.E. direction. Do the following villages which (i) is 6 km East and 4km North from the place lie on the road or no, (ii) is 4km East and 3km North from the place, lie on the road or not?

A car travels due east on a level road for 30 km . It then turns due north at an intersection and travels 40 km before stopping. Find the resultant displacement of the car.

OBJECTIVE RD SHARMA ENGLISH-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Chapter Test
  1. The straight roads intersect at an angle of 60°. A bus on one road is ...

    Text Solution

    |

  2. If the sides of a triangle are in the ratio 3 : 7 : 8, then find R : r

    Text Solution

    |

  3. The area of a regular polygon of n sides is (where r is inradius, R is...

    Text Solution

    |

  4. If the angles of a triangle are 30^(@) and 45^(@), and the included si...

    Text Solution

    |

  5. In a DeltaABC, angleB=(pi)/(3) and angleC=(pi)/(4) let D divide BC in...

    Text Solution

    |

  6. If A is the area and 2s is the sum of the sides of a triangle, then Al...

    Text Solution

    |

  7. If in a triangle ABC, right angled at B, s-a=3, s-c=2, then the values...

    Text Solution

    |

  8. If the sides of a triangle are a, b and sqrt(a^(2) + ab + b^(2)), then...

    Text Solution

    |

  9. In a DeltaA B Csum(b+c)tanA/2tan((B-C)/2)=

    Text Solution

    |

  10. In triangle ABC, angleA=pi/3 and b:c =2:3, tan theta=sqrt3/5, 0 lt the...

    Text Solution

    |

  11. In a DeltaABC, AD is the altitude from A. Given b gt c, angleC=23^(@)"...

    Text Solution

    |

  12. If the angles A, B, C (in that order) of triangle ABC are in arithmeti...

    Text Solution

    |

  13. If the radius of the incircle of a triangle withits sides 5k, 6k and 5...

    Text Solution

    |

  14. Two sides of a triangle are 2sqrt2 and 2sqrt3cm and the angle opposite...

    Text Solution

    |

  15. In a triangleABC, a=13cm, b=12 and c=5cm The distance of A from BC is

    Text Solution

    |

  16. In a triangleABC,B=pi/8, C=(5pi)/(8). The altitude from A to the side ...

    Text Solution

    |

  17. In DeltaABC, A = (2pi)/(3), b -c = 3 sqrt3 cm and " area of " Delta AB...

    Text Solution

    |

  18. In DeltaABC if a=(b-c)sectheta then (2sqrt(bc))/(b-c)sin(A/2)=

    Text Solution

    |

  19. In a DeltaABC, (a + b + c) (b + c - a) = lambda bc. (where symbols ha...

    Text Solution

    |

  20. If in DeltaABC, a=2b and A=3B, then A is equal to

    Text Solution

    |

  21. Let the angles A , Ba n dC of triangle A B C be in AdotPdot and let b ...

    Text Solution

    |