Home
Class 11
MATHS
A straight tunnel is to be made through ...

A straight tunnel is to be made through a mountain. A surveyor observer the two extremities A and B of the tunnel to be built from a point P in front of the mountain. If AP = 3 km, BP = 5 km and `angleAPB = 120^(@)`, then find the length of the tunnel to be built .

Text Solution

Verified by Experts

The correct Answer is:
7km
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRY

    FULL MARKS|Exercise Exercise 3.11|2 Videos
  • TRIGONOMETRY

    FULL MARKS|Exercise Exercise 3.12|20 Videos
  • TRIGONOMETRY

    FULL MARKS|Exercise Exercise 3.9|11 Videos
  • SOLVED PAPER 10

    FULL MARKS|Exercise PART-IV|8 Videos
  • TWO DIMENSIONAL ANALYTICAL GEOMETRY

    FULL MARKS|Exercise Additional Questions Solved|19 Videos

Similar Questions

Explore conceptually related problems

Assume that a tunnel is dug across the earth (radius=R) passing through its centre. Find the time a particle takes to cover the length of the tunnel if (a) it is projected into the tunnel with a speed of sqrt((gR) (b) it is relased from a height R above the tunnel (c ) it is thrown vertically upward along the length of tunnel with a speed of sqrt(gR).

Two soldiers A and B in two different underground bunkers on a straight road, spot an intruder at the top of a hill. The angle of elevation of the intruder from A and B to the ground level in the eastern direction are 30^(@) and 45^(@) respectively. If A and B stand 5 km apart, find the distance of the intruder from B.

Suppose the Government has decided to erect a new Electrical Power Transmission Substation to provide better power supply to two villages namely A and B . The substation has to be on the line l. The distances of villages A and B from the foot of the perpendiculars P and Q on the line l are B from the foot of the perpendiculars P and Q on the line l are 3 km and 5 km respectively and the distance between P and Q is 6 km. (i) What is the smallest length of cable required to connect the two villages. (ii) Find the equations of the cable lines that connect the power station to two villages.(Using the knowledge in conjunction with the principle of reflection allows for approach to solve this problem) .

A tunnel through a mountain for a four lane highway is to have a elliptical opening. The total width of the highway ( not the opening ) is to be 16m , and the height at the edge of the road must be sufficient for a truck 4m high to clear if the highest point of the opening is to be 5m approximately. How wide must the opening be ?

Two long, straight wires a and b are 2*0 m apart, perpendicular to the plane of the paper as shown in figure . The wire a carries a current of 9*6 A directed into the plane of the figure,The magnetic field at the point P at a distance of 10/11 m from the wire b is zero. Find (a) the magnitude and direction of the current in b, (b) the magnitude of the magnetic field B at the point s and (c) the force per unit length on the wire b .

A man starts from a point Aand walks 5km straight ,then turns left at an angle of 60^o further walks 4km in this direction and reaches B.Find how far B is from A.

A factory D is to be connected by a road with a straight railway line on which a town A is situated. The distance D B of the factory to the railway line is 5sqrt(3)k mdot Length A B of the railway line is 20km. Freight charges on the road are twice the charges on the railway. The point P(A P