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Heights and Distances

Math ⇒ Trigonometry

Heights and Distances starts at 10 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Heights and Distances. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.
See sample questions for grade 11
A balloon is flying at a height of 80 m. The angle of elevation from a point on the ground to the balloon is 30°. How far is the balloon from the point on the ground (horizontal distance)?
A flagpole is 20 m high. The angle of elevation of its top from a point on the ground is 30°. How far is the point from the base of the flagpole?
A ladder 10 m long rests against a vertical wall. If the foot of the ladder is 6 m from the wall, what is the angle the ladder makes with the ground?
A man 1.7 m tall observes the top of a building at an angle of elevation of 45°. If he is standing 10 m from the building, what is the height of the building?
A balloon is flying at a height of 80 m. The angle of elevation from a point on the ground to the balloon is 30°. How far is the balloon from the point on the ground (horizontal distance)?
A flagpole is 20 m high. The angle of elevation of its top from a point on the ground is 30°. How far is the point from the base of the flagpole?
A ladder 10 m long rests against a vertical wall. If the foot of the ladder is 6 m from the wall, what is the angle the ladder makes with the ground?
A man 1.7 m tall observes the top of a building at an angle of elevation of 45°. If he is standing 10 m from the building, what is the height of the building?
Which of the following is NOT a step in solving a heights and distances problem? (1) Drawing a diagram (2) Identifying the right triangle (3) Using trigonometric ratios (4) Ignoring the observer’s height
Which of the following is the correct formula for finding the height of an object using the angle of elevation θ and the distance d from the object? (1) height = d × sin θ (2) height = d × cos θ (3) height = d × tan θ (4) height = d / tan θ
Which of the following is true about the angle of depression? (1) It is measured upwards from the horizontal. (2) It is measured downwards from the horizontal. (3) It is always less than 45°. (4) It is always more than 45°.
Which of the following statements is correct? (1) The angle of elevation is always measured from the vertical. (2) The angle of elevation is always measured from the horizontal. (3) The angle of elevation is always 90°. (4) The angle of elevation is always less than 30°.
Fill in the blank: The ______ of an object is the vertical distance from its base to its top.
Fill in the blank: The angle formed between the horizontal and the observer’s line of sight when looking down at an object is called the angle of ______.
Fill in the blank: The ratio of the height of an object to the distance from the observer to the base of the object is equal to the ______ of the angle of elevation.
Fill in the blank: The trigonometric function used to relate the height and base in a right triangle is ______.
True or False: In all heights and distances problems, the ground is assumed to be horizontal unless stated otherwise.
True or False: The angle of elevation and the angle of depression from two different points to the same object are always equal.
True or False: The angle of elevation increases as the observer moves closer to the object.
True or False: The line of sight is always horizontal in problems involving heights and distances.