Unit 5: Height, Distance and Analytical Reasoning - Practice Quiz

1 Which trigonometric ratio relates the opposite side to the adjacent side of a right triangle?

2 Which instrument is commonly used to measure an angle of elevation?

3 When an observer looks upward at an object, the angle formed with the horizontal is called the:

4 When an observer looks downward at an object, the angle formed with the horizontal is called the:

5 A pole casts a shadow m long when the angle of elevation of the Sun is . What is the pole's height?

6 A m ladder rests against a wall with its foot m from the wall. How high does it reach?

7 From a point m from a tower, its angle of elevation is . What is the tower's height?

8 A tree is m high and casts a m shadow. What is the Sun's angle of elevation?

9 A is taller than B, and B is taller than C. Who is the tallest?

10 Ravi walks north and then turns right. In which direction is he now walking?

11 If all pens are stationery items and this object is a pen, what must be true?

12 Maya is older than Neha but younger than Riya. Who is the oldest?

13 Five people sit in a straight row. A sits at the extreme left. What is A's position from the left?

14 P, Q, and R sit in a row facing north. Q sits between P and R, and P sits to Q's left. What is the order from left to right?

15 Four students sit in a row. S is second from the left. What is S's position from the right?

16 A, B, and C sit in a row facing north. A is immediately left of B, and C is immediately right of B. Who sits in the middle?

17 In a circular seating arrangement, people facing the center have their right-hand side in which direction?

18 In a circular seating arrangement, people facing outward have their right-hand side in which direction?

19 Four people sit equally spaced around a circular table. How many immediate neighbors does each person have?

20 A, B, C, and D sit around a circular table facing the center in the clockwise order A, B, C, D. Who sits opposite A?

21 A vertical pole casts a shadow m long when the angle of elevation of the Sun is . What is the height of the pole?

22 From a point m from the base of a tower, its top is observed at an elevation angle of . Find the tower's height.

23 The angle of elevation of the top of a tower from a point m from its base is . What is the height of the tower?

24 A lighthouse is m high. The angle of depression of a boat from its top is . How far is the boat horizontally from the lighthouse?

25 From two points on the same side of a tower and m apart, the elevation angles of its top are and . If the nearer point has the larger angle, find the tower's height.

26 From a point m from a building, the elevation angles of the top of the building and the top of an antenna on it are and , respectively. Find the antenna's height.

27 A person whose eye level is m above the ground observes the top of a building at from a distance of m. What is the building's height?

28 From a point on one bank of a river, the elevation angle of a tree directly opposite is . After moving m directly away from the river, the angle becomes . Find the river's width.

29 Statements: All artists are imaginative. Some teachers are artists. Conclusions: I. Some teachers are imaginative. II. All imaginative people are teachers. Which conclusion follows?

30 Maya ranks th from the top and th from the bottom in a class. How many students are in the class?

31 In a code, each letter is replaced by the letter two positions ahead in the alphabet. Thus, MATH is written as OCVJ. How is LOGIC written?

32 Pointing to a boy, Rina says, "He is the son of the only daughter of my mother." How is Rina related to the boy?

33 Six people P, Q, R, S, T, and U sit in a row facing north. R is at the left end. T is immediately right of R, P is immediately right of T, Q is immediately right of P, and S is at the right end. Who sits between Q and S?

34 Seven people A, B, C, D, E, F, and G sit in a row facing north. A is in the middle, B is second to the left of A, C is immediately right of B, D is at the right end, E is immediately left of D, and F is immediately right of A. Who is at the left end?

35 Five people A, B, C, D, and E sit in a row facing south. C is in the middle. A is second to the left of C, B is immediately to the right of A, and E is at the left end as viewed by you. Who sits immediately to C's left as viewed by you?

36 Eight people K, L, M, N, O, P, Q, and R sit in a row facing north. K is third from the left. L is second to the right of K, M is immediately left of L, N is at the right end, O is second to the left of N, P is immediately right of O, and Q is at the left end. Who is second to the left of M?

37 Six people A, B, C, D, E, and F sit around a circle facing the center. A sits opposite D, B is immediately clockwise from A, C is immediately clockwise from B, and E is immediately clockwise from D. Who sits opposite C?

38 Eight people A, B, C, D, E, F, G, and H sit around a circle facing the center. E sits opposite A. B is second clockwise from A, C is immediately clockwise from B, D is immediately clockwise from A, F is immediately clockwise from E, and G is immediately clockwise from F. Who sits opposite B?

39 Six people J, K, L, M, N, and O sit around a circle facing outward. J sits opposite M. K is immediately to the left of J, L is immediately to the right of M, and N is immediately to the left of M. Who is immediately to the right of J?

40 Eight people K, L, M, N, O, P, Q, and R sit around a circle facing the center. L is second counterclockwise from K, M is immediately clockwise from K, N sits opposite K, O is immediately counterclockwise from N, P is immediately clockwise from N, and Q is immediately clockwise from M. Who sits between M and O?

41 From two points on the same side of a vertical tower, the angles of elevation of its top are and . The points are apart, and the nearer point has the larger angle. What is the tower's height?

42 From a point, the angle of elevation of a tower is . After moving a distance directly toward the tower, the angle becomes , where . Which expression gives the tower's height?

43 A vertical flagstaff stands on a building of height . From a point on level ground, the angles of elevation of the building's roof and the flagstaff's top are and , respectively. What is the flagstaff's height?

44 Two vertical towers of equal height have bases apart. From a point between them, their angles of elevation are and . What is the common height?

45 From the top of a lighthouse, the angles of depression of two boats on the same side are and . The boats are apart. What is the lighthouse's height?

46 A train approaching a tower observes its top at . Ten seconds later, the angle is . If the train maintains constant speed, how much longer will it take to reach the tower's foot?

47 From a point on level ground, the angles of elevation of a building's roof and the top of a flagstaff on it are and . After moving directly away, the angle to the flagstaff's top becomes . What is the building's height?

48 A tree breaks at a point above level ground, and its top touches the ground from the base. Assuming the trunk was vertical before breaking, what was the tree's original height?

49 Six reports are reviewed one at a time. is before both and ; is immediately before ; exactly two reports are between and ; and is after . If is reviewed second, which report must be reviewed sixth?

50 A four-person committee is chosen from . The rules are: requires ; and cannot both serve; exactly one of serves; requires ; and cannot serve with . Which committee is possible?

51 All are . No are . Some are . Every is either or . Which conclusion must follow?

52 Exactly one of five people is responsible for an error, and exactly two statements are true. A says, "The responsible person is not A." B says, "The responsible person is not B." C says, "The responsible person is C or D." D says, "The responsible person is B." E says, "The responsible person is E." Who is responsible?

53 Seven people sit in a row facing north. is third to the right of ; is immediately left of ; is second to the left of ; is at an end; is immediately right of ; and is not adjacent to . Who occupies the central seat?

54 Eight people sit in a row facing north. is fourth to the right of ; is third to the left of ; is second to the left of ; is immediately right of ; is immediately right of ; and is not adjacent to . Who is third from the left?

55 Six people sit in a row, all facing south. is second to the left of ; is immediately to the right of ; is third to the right of ; and occupies the extreme right end as seen by an observer facing the row. Who is second from the observer's left?

56 Eight chairs form a row. Seven people occupy seven chairs, leaving one vacant. is immediately right of ; is immediately right of ; is immediately right of ; is at the right end; is immediately left of ; is at the left end; and the vacant chair is adjacent to . Who occupies the fifth chair from the left?

57 Eight people sit around a circle facing the center. is opposite ; is second clockwise from ; is immediately counterclockwise from ; is opposite ; is immediately clockwise from ; and is opposite . Who is immediately clockwise from ?

58 Eight people sit around a circle, all facing outward. is opposite ; is second to the left of ; is immediately to the right of ; is immediately to the right of ; is opposite ; and is immediately to the left of . Who is opposite ?

59 Eight people sit around a circle facing the center. is opposite ; is second clockwise from ; are consecutive in clockwise order; is opposite ; is immediately clockwise from ; and is not adjacent to . Who is immediately clockwise from ?

60 Eight people sit around a circle facing the center. is opposite ; is second clockwise from ; is immediately clockwise from ; is opposite ; is immediately clockwise from ; and is immediately counterclockwise from . If and exchange seats, who is second clockwise from ?