Class 10 Practice – Level 1 – Some Application of Trigonometry Leave a Comment / By Gulam Hamza / September 24, 2024 Class 10 Practice – Level 1 – Some Application of Trigonometry Total questions: 40 1. In the given figure, the angles of depressions from the observing positions $\displaystyle {{O}_{1}}$ and $\displaystyle {{O}_{2}}$ respectively of the object at A are: Topic: Angles of Depression 30°, 45° 60°, 45° 30°, 60° 60°, 30° None 2. An observer, 1.7 m tall, is 20√3 m away from a tower. The angle of elevation from the eye of observer to the top of tower is 30°. Find the height of tower. Topic: Angle of Elevation 21.8 m 31.7 m 41.9 m 21.7 m None 3. A pole casts a shadow of length 2√3 m on the ground, when the sun's elevation is 60°. Find the height of the pole. Topic: Height Using Angle of Elevation 6 m 10 m 15 m 4 m None 4. From the top of a tower of height 50 m, find the angles of depression of the top and bottom of a pole are 30° and 45° respectively. Find the height of the pole. (Use √3=1⋅732 ) Topic: Angles of Depression 41.13 m 21.13 m 36.13 m 22.13 m None 5. A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower. Topic: Angle of Elevation 35√4 m 65√8 m 15√3 m 18√3 m None 6. An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45° What is the height of the chimney? Topic: Angle of Elevation 30 m 50 m 60 m 80 m None 7. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30° . Topic: Rope and Angle with Ground 15 m 20 m 25 m 10 m None 8. From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of the tree is 35º. Find the height of the tree. Topic: Angle of Elevation 42.06 ft 32.90 ft 50.90 ft 43.50 ft None 9. A vertical pole stands on the level ground. From a point on the ground, 25 m away from the foot of the pole, the angle of elevation of its top is found to be 60°. Find the height of the pole. [Take √3=1.732.] Topic: Angle of Elevation 32.3 m 56.2 m 43.3 m 56.3 m None 10. A kite is flying, attached to a thread which is 165 m long. The thread makes an angle of 30° with the ground. Find the height of the kite from the ground, assuming that there is no slack in the thread. Topic: Height using Trigonometry 82.5 m 25.3 m 65.2 m 45.6 m None 11. A kite is flying at a height of 75 m from the level ground, attached to a string inclined at 60° to the horizontal. Find the length of the string, assuming that there is no slack in it. (in metres)[Take√3 =1.732.] Topic: Properties of Length 50√3 m 30√3 m 80√3 m 60√3 m None 12. The ratio of the length of a rod and its shadow is 1: $\displaystyle \dfrac{1}{{\sqrt{3}}}$ . What is the angle of elevation of the source of light? Topic: Angle of Elevation 60° 30° 40° 35° None 13. The height of a tower is 10 m. Calculate the length of its shadow, when the sun's altitude is 45°. Topic: Properties of Length 10 m 12 m 15 m 18 m None 14. If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is the angle of elevation of the sun? Topic: Angle of Elevation 80° 60° 150° 30° None 15. A 8 foot metal guy wire is attached to a broken stop sign to secure its position until repairs can be made. Attached to a stake in the ground, the guy wire makes an angle of 51º with the ground. How far from the foot of the stop sign is the stake? Topic: Properties of Distance 5.03 ft 4.25 ft 6.71 ft 7.80 ft None 16. On a windy day, a 90 foot rope tightly secures a hot air balloon to a stake in the ground. From the balloon, the angle of depression of the stake is 62º. Find the height of the balloon, assuming the wind to be constant. Topic: Properties of Height 85.8 ft 68.6 ft 79.5 ft 97.5 ft None 17. From point P on the ground, the angle of elevation of an airplane is 23º. The altitude of the plane is 1200 meters. What is the distance from point P to the airplane? Topic: Properties of Distance 2862 m 1257 m 3069 m 2827 m None 18. As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30º and 45º. If one ship is exactly behind the other on the same side of the light house, the distance between the two ships. [Use √3 = 1.732] Topic: Properties of Distance 73.2 m 63.2 m 36.2 m 43.2 m None 19. A ladder 15 m long makes an angle of 60° with the wall. Find the height of the point where the ladder touches the wall. Topic: Properties of Height 7.5 m 6.5 m 8.5 m 9.5 m None 20. The shadow of a tower at a time is three times as long as its shadow when the angle of elevation of the sun is 60°. Find the angle of elevation of the sun at the time of the longer shadow. Topic: Angle of Elevation 35° 65° 30° 60° None 21. A plane has traveled 26 miles on a course heading 48º east of north. How far north (x) has the plane traveled at this point? Topic: Properties of Distance 17.4 miles 25.6 miles 19.9 miles 40.5 miles None 22. If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is the angle of elevation of the sun? Topic: Angle of Elevation 80° 60° 120° 40° None 23. Two men on either side of a 75 m high building and in line with base of building observe the angles of elevation of the top of the building as 30 ∘ and 60 ∘ . Find the distance between the two men. (Use√3=1.73 ) Topic: Angle of Elevation and Distance 145 m 178 m 173 m 155 m None 24. A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 5 m. From a point on the ground the angles of elevation of the top and bottom of the flagstaff are 60 ∘ and 30 ∘ respectively. Find the height of the tower and the distance of the point from the tower. (Use √3 =1.732) Topic: Angle of Elevation 6.32 m 45.6 m 78.3 m 4.33 m None 25. A student lets out 100 feet of string on a kite from a hand height of 3 feet. The angle between horizontal hand height and the kite is 25º. Find the height of the kite above the ground. Topic: Height Using Angle of Elevation 50.25 ft 45.26 ft 70.21 ft 80.05 ft None 26. The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building. Topic: Height Using Angle of Elevation 20 m 30 m 40 m 80 m None 27. The ratio of the length of a vertical rod and the length of its shadow is 1:√3 . Find the angle of elevation of the sun at that moment? Topic: Angle of Elevation 40° 50° 80° 30° None 28. The rod AC of a TV disc antenna is fixed at right angles to the wall AB and a rod CD is supporting the disc as shown in Fig. If AC=1.5 m long and CD=3 m, find (i) tanθ (ii) secθ+cosecθ Topic: Trigonometric ratios in a right-angled $\displaystyle \dfrac{1}{√3}$, $\displaystyle \dfrac{2}{√3}$ + 2 $\displaystyle \dfrac{2}{√3}$ , $\displaystyle \dfrac{5}{√3}$ + 8, $\displaystyle \dfrac{1}{√3}$ , $\displaystyle \dfrac{6}{√3}$ + 9 $\displaystyle \dfrac{2}{√3}$ , $\displaystyle \dfrac{2}{√3}$ +5 None 29. A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 6 m. At a point on the plane, the angle of elevation of the bottom and top of the flag-staff are 30° and 45° respectively. Find the height of the tower. (Take√3 =1.73 ) Topic: Properties of Height 8.23 m 6.56 m 8.19 m 89.5 m None 30. A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the angle of elevation of the top of the light house from 60° to 30°. Find the speed of the boat in metres per minute. [ Use √3=1.732] Topic: Angle of Elevation 57.73 m/min. 67.00 m/min. 26.53 m/min. 89.73 m/min. None 31. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60°, and the angle of depression of its foot is 45°. Find the height of the tower. Given that √3 =1.732. Topic: Height Using Angle of Elevation 19.124 m 19.457 m 14.124 m 56.234 m None 32. From the top of a 108 foot lighthouse, the angle of depression of a boat at sea is 27º. Find the horizontal distance from the boat to the base of the lighthouse. Topic: Angle of Depression And Distance 239.05 ft 212.18 ft 204.22 ft 265.15 ft None 33. The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30° than when it was 60°. Find the height of the tower. (Given√3=1.732 ) Topic: Properties of Height 78.64 m 65.64 m 45.64 m 34.64 m None 34. The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number. Topic: Angle of Depression And Distance 95 m 85 m 65 m 36 m None 35. The angle of elevation from a point P of the top of a tower QR,50 m high is 60° and that of the tower PT from a point Q is 30°. Find the height of the tower PT, correct to the nearest meter. Topic: Height using Angle of Elevation and Depression 17 cm 20 cm 35 cm 25 m None 36. A shopper is standing on level ground 800 feet from the base of a 250 foot tall department store. The shopper looks up and sees a flag on the store's roof. To the nearest degree what is the angle of elevation to the top of the building from the point on the ground where the shopper is standing? Topic: Angle of Elevation 17° 23° 45° 33° None 37. From the hay loft door, Sid sees his dog on the ground. The angle of depression of the dog is 40º. Sid's eye level is 16 feet above the ground. How many feet must the dog walk to reach the open barn door directly below Sid? Topic: Angle of Depression And Distance 25 ft 19 ft 38 ft 50 ft None 38. A flag pole 18 feet tall casts a shadow 12 feet long at a specific time of day. Find the angle of elevation of the sun at this time of day. Topic: Angle of Elevation 54º 46º 56º 65º None 39. An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45° . What is the height of the chimney? Topic: Height Using Angle of Elevation 40 m 60 m 50 cm 30 m None 40. From the top of a cliff 20 m high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of the tower. Then, find height of the tower. Topic: Height Using Angle of Elevation 20 m 60 m 40 m 80 m None 1 out of 40 Time's up
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