Applications of Trigonometric MCQ Test 1

1. A ladder is leaning against a wall. If the ladder is 20 meters long and forms an angle of 80° with the ground, how high up the wall does the ladder reach?

2. A boat is sailing towards a lighthouse. If the angle of elevation to the top of the lighthouse is 15° and the boat is 500 meters away from the lighthouse, how tall is the lighthouse?

3. A car is driving downhill on a road with a slope of 18°. If the car covers a horizontal distance of 500 meters, how much vertical distance does it descend?

4. In a right-angled triangle, if one acute angle measures 60° and the hypotenuse is 6 meters long, what is the length of the side opposite the 60° angle?

5. A person is flying a kite with a string that makes an angle of 75° with the ground. If the person is holding the kite 60 meters above the ground, how long is the string?

6. A roller coaster has a drop that forms a 60° angle with the ground. If the vertical height of the drop is 40 meters, what is the horizontal distance traveled by the coaster?

7. A mountain climber is on a cliff. If the angle of elevation to the peak of the mountain is 60° and the climber is 200 meters above sea level, how high is the mountain peak?

8. A playground slide has a length of 8 meters and makes an angle of 30° with the ground. What is the vertical height of the slide?

9. A ladder is leaning against a wall. If the ladder is 15 feet long and forms a 60° angle with the ground, how high up the wall does the ladder reach?

10. A person is standing on the roof of a skyscraper. If the angle of depression to a point on the ground is 75° and the building is 150 meters tall, how far is the point from the base of the building?

11. A ladder is placed against a wall. If the ladder is 25 meters long and forms a 30° angle with the ground, how high up the wall does the ladder reach?

12. An airplane is flying at an altitude of 12,000 meters. If the angle of elevation from a ground observer to the airplane is 50°, how far is the airplane from the observer?

13. A ladder is leaning against a building. If the ladder is 20 meters long and forms a 75° angle with the ground, how high up the building does the ladder reach?

14. A radar dish rotates counterclockwise at a rate of 0.1 revolutions per second. If the dish has a radius of 15 meters, what is the linear speed of a point on the edge of the dish?

15. The angle of elevation to the top of a building is 40°. If a person is standing 45 meters away from the base of the building, how tall is the building?

16. A ship travels due east for 120 kilometers, then changes its course and travels due north for 160 kilometers. What is the straight-line distance from the starting point to the final position of the ship?

17. A car is parked on a hill with a slope of 10°. If the car is 100 meters away from a point directly below it on the hill, how high is the hill?

18. A tower casts a shadow of 60 meters when the sun's angle of elevation is 25°. What is the height of the tower?

19. A telescope is positioned on top of a mountain. If the angle of depression to a star is 85° and the mountain is 4,000 meters tall, what is the distance from the star to the mountain's base?

20. A building casts a shadow of 30 meters when the sun's angle of elevation is 50°. What is the height of the building?

21. A roller coaster has a loop with a radius of 30 meters. If the roller coaster travels through the loop at a speed of 20 m/s, what is the acceleration experienced by a rider at the top of the loop?

22. A building casts a shadow of 40 meters when the sun's angle of elevation is 30°. What is the height of the building?

23. A flagpole casts a shadow of 12 meters when the sun's angle of elevation is 30°. What is the height of the flagpole?

24. The angle of depression from the top of a hill to a point on the ground is 18°. If the hill is 80 meters tall, how far is the point from the base of the hill?

25. A triangular piece of land has sides measuring 40 meters, 60 meters, and 80 meters. What is the measure of the largest angle in the triangle?

26. A car is driving uphill on a road with a slope of 12°. If the car covers a horizontal distance of 200 meters, how much vertical distance does it gain?

27. A ladder is placed against a vertical wall. If the ladder is 10 meters long and makes an angle of 60° with the ground, how far is the base of the ladder from the wall?

28. An observer is standing 30 meters away from a building. If the angle of elevation to the top of the building is 45°, how tall is the building?

29. In a right-angled triangle, if one acute angle measures 30° and the hypotenuse is 10 meters long, what is the length of the side opposite the 30° angle?

30. The angle of depression from the top of a building to a point on the ground is 40°. If the building is 20 meters tall, how far is the point from the base of the building?

31. A soccer field has a goalpost at each corner. If the distance between the goalposts along the length of the field is 100 meters and the width of the field is 50 meters, what is the angle between the goalposts at one end?

32. A ladder is leaning against a wall. If the ladder is 15 meters long and forms an angle of 70° with the ground, how high up the wall does the ladder reach?

33. A flagpole casts a shadow of 20 meters when the sun's angle of elevation is 40°. What is the height of the flagpole?

34. A person is standing on a cliff. If the angle of depression to a boat on the water is 40° and the person is 50 meters above sea level, how far is the boat from the base of the cliff?

35. A flagpole casts a shadow of 25 meters when the sun's angle of elevation is 60°. What is the height of the flagpole?

36. An archer aims an arrow at a target. If the arrow leaves the bow at an angle of 25° and the target is 70 meters away, what is the horizontal distance the arrow travels before hitting the target?

37. In a right-angled triangle, if one acute angle measures 45° and the hypotenuse is 8 meters long, what is the length of the side opposite the 45° angle?

38. A person is standing on a hill with an angle of elevation of 25°. If the person looks down and sees a tree, the angle of depression to the top of the tree is 10°. If the hill is 50 meters tall, how tall is the tree?

39. A Ferris wheel has a radius of 25 meters. If the wheel completes two full revolutions, how far does a point on the edge of the wheel travel?

40. A Ferris wheel has a radius of 15 meters. If the wheel completes one full revolution, how far does a point on the edge of the wheel travel?

41. In a right-angled triangle, if one acute angle measures 75° and the hypotenuse is 12 meters long, what is the length of the side opposite the 75° angle?

42. An airplane is flying at an altitude of 10,000 meters. If the angle of elevation from a ground observer to the airplane is 30°, how far is the airplane from the observer?

43. A ship at sea spots a lighthouse. The angle of elevation to the top of the lighthouse is 20°. If the ship is 3,000 meters away from the lighthouse, how tall is the lighthouse?

44. A Ferris wheel has a radius of 10 meters and rotates at a constant rate. If a passenger is 15 meters above the ground after 20 seconds, what is the angular velocity of the Ferris wheel in radians per second?

45. The angle of elevation to the top of a tower is 20°. If a person is standing 60 meters away from the base of the tower, how tall is the tower?

46. A person is flying a kite with a string that makes an angle of 45° with the ground. If the person is holding the kite 40 meters above the ground, how long is the string?

47. A wheel with a radius of 5 meters is rotating at a constant rate. If a point on the edge of the wheel travels a distance of 10π meters in one minute, what is the angular velocity of the wheel in radians per second?

48. The angle of elevation to the top of a mountain is 15°. If a person is standing 100 meters away from the base of the mountain, how tall is the mountain?

49. A bridge spans a river with a width of 100 meters. If the bridge forms an angle of 15° with the riverbanks, how long is the bridge?

50. A ski slope descends at an angle of 45°. If a skier covers a horizontal distance of 800 meters, what is the vertical drop in elevation?