Home
Class 10
MATHS
In the window of a house, there is a lad...

In the window of a house, there is a ladder at an angle of `60^(@)` with the ground. If the ladder is `2sqrt(3)` m long, then calculate with figure, the height of the window above the ground.

Text Solution

Verified by Experts


Let the height of the ground be AB. Then the right-angled triangle ABC, we get,
`sin60^(@)=(AB)/(AC)`[ by the definition of `sin theta`]
or, `(sqrt(3))/(2)=(AB)/(2sqrt(3)) or, AB=3`
Hence the window is 3 m high above the ground.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE|66 Videos
  • THEOREMS RELATED TO TANGENT IN A CIRCLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE 4.2|23 Videos
  • TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE|28 Videos

Similar Questions

Explore conceptually related problems

If the angle of elevation of a kite is 60^(@) and the length of thread is 20sqrt(3) metres, calcluate the height of kite above the ground.

A ladder is placed against a wall which is inclined at an angle 60^@ with the ground. The foot of the ladder is 4.6m. Away from the wall. Then the length of the ladder is

Fill n the blanks if the angle of elevation a kite is 60^@ and the length of thread is 20sqrt3 metres, then the height of kite above the ground is____.

A child pulls a rope attached to a stone with a force of 60 N . The rope makes an angle of 40^@ with the ground . (a) Calculate the effective value of the pull tending to move the stone along the ground.

Two houses stand just on the opposite sides of a road of a village. A ladder that stands against the wall of the first house is at a distance of 6 metres from the house and makes an angle of 30^(@) with the horizontal line.But if the ladder stands against the wall of the second house keeping its foot at the same point, it makes an angle of 60^(@) with the horizontal line. (a) Find the length of the ladder. (b) Calculate the distance of the foot of the ladder from the foot of the wall of the second house. (c) Find the width of the road. Find the height where the top of the ladder is fixed against the wall of the second house.

If the angle of elevation of a kite is 60^@ and the length of the string is 80sqrt3 metre, then the height of the kite from the ground is

A wire of length 18 m had been tied with electric pole at an angle of elevation 30^(@) with the ground. Because it was covering a long distance, it was cut and tied at an angle of elevation 60^(@) with the ground. How much length of the wire was cut?

Shib is flying kite having the length of thread 250 metres, when the thread makes an angle 60^(@) with the horizontal line and when the thread makes an angle of 45^(@) with the horizontal line. Calculate in each case what is the height of kite from the ground. Also find in which of the two cases will the kite be at a greater height from the other.

An electrician wants to repair an electric connection on a pole of height 9 m. He needs to reach 1.8 m below the top of the pole to do repair work. What should be the length of the ladder which he should use, when he climbs it at an angle of 60^(@) with the ground? What will be the distance between foot of the ladder and foot of the pole?

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground by making 30^(@) angle with the ground. The distance between the foot of the tree and the top of the tree on the ground is 8 m. Find the height of the tree before falling down.

CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES -EXERCISE
  1. In the window of a house, there is a ladder at an angle of 60^(@) with...

    Text Solution

    |

  2. If tan theta=(p)/(q), what is the value of (p sec theta-q " cosec" t...

    Text Solution

    |

  3. In DeltaABC, right angled at B, AB:AC=1:sqrt(2), then (2 tan A)/(1-ta...

    Text Solution

    |

  4. (sin30^(@)cos45^(@))/(tan 60^(@)) is equal to

    Text Solution

    |

  5. In DeltaABC, If angleC=90^(@), angleA=60^(@) and AB=40 cm, then AC is ...

    Text Solution

    |

  6. Write true of false : cot theta=(cos theta)/(sin theta)

    Text Solution

    |

  7. Write true of false : sin theta is a product of sin and theta.

    Text Solution

    |

  8. Fill in the blanks : The trigonometric ratio cos theta= ul(" ...

    Text Solution

    |

  9. Fill in the blanks : The value of sin theta can never be greate th...

    Text Solution

    |

  10. Fill in the blanks : The value of cot 0^(@) is not .

    Text Solution

    |

  11. Find the value of cos(-1170^(@)).

    Text Solution

    |

  12. Calculate the value of sec(-1680^(@)) sin 330^(@).

    Text Solution

    |

  13. Simplify : sin 300^(@) cos 390^(@) tan (-855^(@))+cos(-120^(@))* sin ...

    Text Solution

    |

  14. Prove that tan 225^(@) cot 405^(@)+tan 765^(@) cot 675^(@)=0.

    Text Solution

    |

  15. Evalute : "sin"^(2)(pi)/(4) + "cos"^(2) (3pi)/(4)+"cos"^(2)(5pi)/(4)...

    Text Solution

    |

  16. Prove that "tan"(pi)/(12) "tan"(pi)/(16) "tan"(5pi)/(12)"tan"(7pi)/(1...

    Text Solution

    |

  17. If tan 35^(@)=x, then prove that (tan 145^(@)- tan 125^(@))/(1+tan14...

    Text Solution

    |

  18. Find the value of sin^(3)60^(@) cot 30^(@)-2 sec^(2) 45^(@)+3 cos60^(@...

    Text Solution

    |

  19. If (cos theta)/(1-sin theta)-(costheta)/(1+sin theta)=2, then find the...

    Text Solution

    |

  20. If (cos x)/(cosy)=n and (sinx)/(siny)=m, what is the value of (m^(2)...

    Text Solution

    |

  21. If x cos 60^(@)+y cos0^(@)=3 and 4x sin 30^(@) -y cot 45^(@)=2, then ...

    Text Solution

    |