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 10
What is the angle of elevation?
A man observes the top of a tower at an angle of elevation of 30°. He then walks 40 m towards the tower and finds the angle of elevation to be 60°. Find the height of the tower.
A man standing at a certain distance from a tower finds the angle of elevation of the top of the tower to be 45°. If he moves 30 m farther from the tower, the angle of elevation becomes 30°. Find the height of the tower.
A man standing on the roof of a building 50 m high observes a car on the road at an angle of depression of 28°. How far is the car from the base of the building? (Round your answer to the nearest meter.)
A balloon is flying at a height of 100 m. The angle of elevation from a point on the ground is 30°. How far is the point from the balloon (horizontal distance)?
A flagpole is 12 m high. If the angle of elevation of its top from a point on the ground is 45°, how far is the point from the base of the flagpole?
A ladder 15 m long rests against a wall. The foot of the ladder is 9 m from the wall. Find the angle the ladder makes with the ground (to the nearest degree).
A man 1.6 m tall observes the top of a tower at an angle of elevation of 45°. If the distance between the man and the tower is 30 m, what is the height of the tower?
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 the Pythagorean theorem (4) Ignoring the angles involved
Which of the following is NOT required to solve a heights and distances problem? (1) Angle of elevation or depression (2) Length of the shadow (3) Color of the object (4) Distance from the object
Which of the following is the correct definition of the angle of depression? (1) The angle between the horizontal and the line of sight to an object below the horizontal (2) The angle between the vertical and the line of sight to an object above the horizontal (3) The angle between two objects (4) The angle between the ground and the object
Which of the following is the correct formula for the tangent of an angle in a right triangle? (1) Opposite/Adjacent (2) Adjacent/Opposite (3) Hypotenuse/Opposite (4) Hypotenuse/Adjacent
Fill in the blank: In heights and distances, the observer's eye level is usually considered as the ________ line.
Fill in the blank: The ________ is the straight line from the observer’s eye to the object being observed.
Fill in the blank: The ________ of an object is the length of its shadow when the sun is at a certain angle of elevation.
Fill in the blank: The ________ of elevation is the angle between the horizontal and the line of sight to an object above the horizontal.
True or False: In all heights and distances problems, the observer and the object are always at the same horizontal level.
True or False: The angle of depression is always measured from the horizontal downward.
True or False: The angle of elevation and the angle of depression are always measured from the horizontal.
True or False: The angle of elevation and the angle of depression from two different points to the same object are always equal.
