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

1 The angle formed between the horizontal line and the line of sight to an object above the observer is called the:

2 The angle formed between the horizontal line and the line of sight to an object below the observer is called the:

3 Which trigonometric ratio is defined as ?

4 A pole casts a shadow of length m. If the height of the pole is also m, what is the angle of elevation of the sun?

5 If the angle of elevation of the top of a building is , the observer is:

6 A person standing m from a tree observes its top at an angle of elevation of . Assuming the person's eye level is ignored, what is the height of the tree?

7 In a right-angled triangle used for height and distance problems, the side opposite the right angle is called the:

8 In a linear seating arrangement, people are seated:

9 If A is sitting immediately to the left of B, who is sitting immediately to the right of A?

10 Five students sit in a row. How many students are sitting at the extreme ends?

11 If P is at the left end of a row and Q is at the right end, who is sitting between them?

12 A, B, and C sit in a row. B sits between A and C. Which arrangement is possible?

13 Six people sit in a row. If R is third from the left, what is R's position from the right?

14 If M sits immediately between L and N in a row, which statement is true?

15 In a circular seating arrangement, the people are seated:

16 In a circular arrangement, the person sitting immediately next to another person is called that person's:

17 If A and B sit opposite each other in a circle, what is the relationship between their positions?

18 Four people sit around a circular table. How many people are immediate neighbors of any one person?

19 When people face the center of a circle, a person's left side is generally in which direction around the circle?

20 Six people sit around a circular table. If X sits second to the right of Y, how many people are between X and Y in that direction?

21 From a point m away from the foot of a tower, the angle of elevation of its top is . What is the height of the tower?

22 The angle of elevation of the top of a tower is . After moving m toward the tower, the angle becomes . Find the height of the tower.

23 From a point m from a building, the angles of elevation of the top of the building and the top of an antenna mounted on it are and , respectively. What is the height of the antenna?

24 From the top of a lighthouse, the angle of depression of a boat located m horizontally from its foot is . Find the height of the lighthouse.

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

26 Two observers are on opposite sides of a tower and are m apart. The angles of elevation of the top are and . If the foot of the tower lies between them, what is the tower's height?

27 A person whose eye level is m above the ground observes the top of a tower at an elevation angle of . The person is m from the tower. What is the tower's height?

28 Seven people A, B, C, D, E, F, and G sit in a row facing north. C sits in the middle. A sits second to the left of C, and D sits immediately to the right of A. E sits immediately to the right of C. B sits at an end and to the left of A. G sits to the right of F. Who occupies the sixth seat from the left?

29 Eight people P, Q, R, S, T, U, V, and W sit in a row facing north. R is third from the left. T is second to the right of R, and P is immediately to the left of T. W is at the right end, with Q immediately to its left. S is to the left of R but not at an end. U is to the right of P. What is the complete order from left to right?

30 Six people A, B, C, D, E, and F sit in a row facing north. B is third from the left, and A sits immediately to the left of B. E sits at the left end, while F sits at the right end. C sits immediately to the right of D. What is C's position from the left?

31 Nine people sit in a row facing north. M is third from the right. K is fourth to the left of M. L is second to the right of K, and N is immediately to the left of L. How many people sit between N and M?

32 Ten people sit in a row. A is fourth from the left, and B is fifth from the right. C sits exactly midway between A and B. What is C's position from the left?

33 In a row of people facing north, R is fifth from the left. S sits three places to the right of R. What is S's position from the right?

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

35 Eight people sit around a circular table facing the center. B sits second clockwise from A. C sits opposite A, and D sits immediately anticlockwise from C. What is D's position relative to B?

36 Six people P, Q, R, S, T, and U sit around a circular table facing the center. R sits second clockwise from P, and S sits opposite P. What is S's position relative to R?

37 Eight people A, B, C, D, E, F, G, and H sit around a circular table facing the center. B sits immediately clockwise from A. D sits second clockwise from B. E sits opposite A. G sits second clockwise from E. H sits immediately anticlockwise from A. C sits between B and D. Who sits opposite D?

38 Seven people A, B, C, D, E, F, and G sit around a circular table facing the center. B sits second clockwise from A, and C sits immediately clockwise from B. D sits second anticlockwise from A, with E immediately anticlockwise from D. F sits immediately clockwise from A. Who are the immediate neighbors of A?

39 Eight people A, B, C, D, E, F, G, and H sit around a circular table facing the center. E sits opposite A. B sits immediately clockwise from A, C sits immediately clockwise from B, and D sits immediately clockwise from C. Who sits second anticlockwise from E?

40 Six people P, Q, R, S, T, and U sit around a circular table facing the center. Q sits immediately clockwise from P, R sits immediately clockwise from Q, S sits opposite P, and T sits immediately anticlockwise from P. Who sits opposite Q?

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

42 Two observers stand on opposite sides of a vertical tower. The distance between them is m, and their angles of elevation of the top are and . Find the height of the tower.

43 From a point on the roof of a building, the angle of depression of the foot of a tower is , while the angle of elevation of its top is . If the horizontal distance between the building and the tower is m, what is the height of the tower?

44 A vertical pole breaks at some point, and its upper part touches the ground m from the foot of the pole. The broken part makes an angle of with the ground. What was the original height of the pole?

45 Two vertical towers of heights m and m stand m apart. From a point between their feet, their tops have the same angle of elevation . What is ?

46 A person walks m directly toward a tower. During the walk, the angle of elevation of the top changes from to . Assuming level ground and negligible eye height, find the height of the tower.

47 As the sun's angle of elevation decreases from to , the shadow of a vertical tower becomes m longer. What is the height of the tower?

48 Eight people through sit in a row facing north. The following conditions apply: is third to the right of ; is second to the left of ; is immediately right of ; is immediately left of ; exactly one person sits between and ; and sits to the left of . Which order from left to right is possible?

49 Nine people through sit in a row facing north. occupies the middle seat. is third to the left of , and is third to the right of . is immediately right of , is immediately left of , and is immediately right of . If and occupy the left and right ends respectively, who sits immediately to the left of ?

50 Eight people sit in a row. face north, while face south. is second to the right of . is immediately to the right of . is immediately to the right of . is immediately to the left of . is immediately to the left of . is immediately to the right of , and is immediately to the left of . Who is immediately to the left of from 's perspective?

51 Seven people through occupy seven of nine seats in a row, all facing north. occupies the middle seat. is immediately left of , and is immediately left of . is second to the left of . is immediately right of . is second to the right of , and is immediately right of . Which seats, numbered from left to right, are vacant?

52 Eight people through sit in a row facing north. is second to the right of . is immediately right of . is immediately right of , and is immediately right of . sits to the right of , is not adjacent to , and is not adjacent to . Which order from left to right is possible?

53 Ten people through sit in a row facing north. and occupy the two ends. is immediately right of . is third to the right of . is immediately left of , and is immediately left of . is immediately right of . is second to the right of , with between and . is immediately right of . Who is fifth to the right of ?

54 Eight people through sit in a row facing north. occupies the right end. is second from the left. is third to the right of . is immediately left of , and is immediately left of . is immediately right of , and is immediately right of . sits to the left of . Who is fourth to the right of ?

55 Eight people through sit around a circular table facing the center. sits opposite . is second clockwise from , with between them. is immediately clockwise from . is immediately clockwise from , and sits between and . Who sits opposite ?

56 Eight people through sit around a circle, all facing outward. is immediately to the left of , while is immediately to the right of . is immediately to the right of , and is immediately to the right of . sits opposite . is immediately to the right of , and is immediately to the right of . Who is second to the left of ?

57 Seven people through sit around a circular table facing the center. is immediately clockwise from . sits between and , with both adjacent to . is immediately clockwise from . is immediately clockwise from , and is immediately clockwise from . Who is second clockwise from ?

58 Seven people through occupy seven of eight equally spaced chairs around a circular table, all facing the center. One chair is vacant. is second clockwise from , and is immediately clockwise from . sits opposite , and is immediately clockwise from . is immediately counterclockwise from , while sits between and . Who sits opposite ?

59 Six people through sit around a circular table. face the center, while face outward. sits opposite . is immediately clockwise from , is immediately clockwise from , and is immediately clockwise from . Who is second to the left of from 's perspective?

60 Eight people through sit around a circular table facing the center. is second clockwise from , and is immediately clockwise from . sits opposite , and is immediately clockwise from . is immediately counterclockwise from , while sits between and . Which clockwise order, starting from , is possible?