Trigonometry

Gap-fill exercise

  
Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!
1. The height of a tower is 10 m. The length of its shadow when Sun's altitude is 45° is m.
2. If the ratio of the height of a tower and the length of its shadow is 3 : 1, then the angle of elevation of the Sun (in °) is .
3. The angle of elevation of the Sun (in °) when the length of the shadow of a vertical pole is equal to its height is .
4. If the angle of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary, the heoght of the tower is m.
5. The is the line drawn from the eyes of an observer to a point in the object viewed by the observer.
6. The angle of is the angle formed by the line of sight with the horizontal, when it is above the horizontal level.
7. The ratio of the length of a rod and its shadow is 1 : 3. The angle of elevation of the Sun (in °) is .
8. From the top of a cliff 25 m high the angle of elevation of the tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is m.
9. The angle of is the angle formed by the line of sight with the horizontal when it is below the horizontal.
10. The tops of two poles of height 16 m and 10 m are connected by a wire of length l metres. If the wire makes an angle of 30° with the horizontal, then l = .