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Question

Find the length of the ladder if the angle of elevation of the ladder against a wall is 60° and the foot of the ladder is 11.5 m away from the wall.

The correct answer is
23 m

Angle with ground = 60°

⇒ cos 60° = Base / Ladder = 1/2

⇒ Ladder = Base ÷ (1/2) = 11.5 × 2

⇒ Ladder = 23 m

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Important Questions from Heights and Distances

  1. If x is the distance of P from the bottom of the pillar, then consider the following statements :

    1. x can take two values which are in the ratio 1 : 3

    2. x can be equal to the height of the flagstaff

    Which of the statements given above is/are correct?

  2. What is a possible value of tan θ ? 

  3. A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. From a point on the field, the angles of elevation of the bottom and tip of the flag staff are 30° and 45° respectively. Which one of the following gives the best approximation to the height of the tower?

  4. Two poles are 10 m and 20 m high. The line joining their tops makes an angle of 15° with the horizontal. The distance between the poles is approximately equal to

  5. The angle of elevation of the top of a tower from a point 20 m away from its base is 45 °. What is the height of the tower?

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