/20 1234567891011121314151617181920 Test Code: MC9L3 1 / 20 1. A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are α and β respectively. Find the height of the tower. A) None of these B) tan α/tan β – tan α C) tan α/tan β D) h tan α/tan β – tan α 📝 Solution: 2 / 20 2. The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. Find the distance between the two towers and also the height of the tower. A) distance = 7√3 m, height = 10 m B) distance = 7√3 m, height = 5 m C) distance = 10√3 m, height = 10 m D) distance = 10√5 m, height = 13 m 📝 Solution: 3 / 20 3. If a man standing on a plat form 3 m above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection. A) True B) False 📝 Solution: 4 / 20 4. A balloon observed from 2 m and 6 m above ground has angles of elevation 60° and 30°. Find balloon’s height. A) 6 cm B) 12 cm C) 8 cm D) 10 cm 📝 Solution: 5 / 20 5. An observer 1.5 m tall is 20.5 m away from a tower 22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer. A) 30° B) 60⁰ C) 45⁰ D) 90° 📝 Solution: 6 / 20 6. The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Find the height of the tower ? A) √st B) st² C) None of these D) st 📝 Solution: 7 / 20 7. A tree 10(2 + √3) metres high is broken by the wind at a height 10√3 metres from its root in such a way that top struck the ground at certain angle and horizontal distance from the root of the tree to the point where the top meets the ground is 10m Find the angle of elevation made by top of the tree with the ground. A) 60⁰ B) 80⁰ C) 45° D) 75⁰ 📝 Solution : Consider the given figure, AC = 10(2 + √3) – 10√3 = 20 m (Hypotenuse) Hence sin(∠C ) = (AB)/(AC) = (10√3)/20 = √3/2 = Sin 60⁰ Hence ∠C = 60⁰ Hence the angle of elevation made by top of the tree with the ground is 60⁰ 8 / 20 8. From the top of a tower h m high, angles of depression of two objects, which are in line with the foot of the tower are a and β (β > a). Find the distance between the two objects. A) h (cot α + cot β) B) h (cot α – cot β) C) None of these D) (cot α – cot β)/h 📝 Solution: 9 / 20 9. Find the angle of elevation of the sun when the shadow of a pole h m high is √3 h m long. A) 75⁰ B) 30° C) 55⁰ D) 60⁰ 📝 Solution 10 / 20 10. The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 m towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower. A) 9 (√3) m B) 10 (√3 + 1) m C) 8 (√3 + 1) m D) 5 (√3 + 5) m 📝 Solution: 11 / 20 11. The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Find the height of the tower. A) 7√16 B) 22/√3 C) 25√3 D) √25/3 📝 Solution: 12 / 20 12. A window of a house is h m above the ground. Form the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be a and p, respectively. Find the height of the tower. A) h(1+tanα cot β) m B) (1+tanα cot β)/h m C) None of these D) tanα cot β m 📝 Solution: 13 / 20 13. A ladder 15 m long just reaches the top of a vertical wall.If the ladders makes an angle of 60° with the wall,then find the height of the wall. A) 13/2 B) 9/5 C) 8/3 D) 15/2 m 📝 Solution: 14 / 20 14. If the length of the shadow of a tower is increasing, then the angle of elevation of the Sun is also increasing. A) True B) False 📝 Solution: 15 / 20 15. The angles of elevation of an aeroplane flying vertically above the ground from two consecutive milestones (1 km) apart are 450 and 600. The height of the aeroplane from the ground is A) (√3 + 1) km B) 1/2 (3 + √3) km C) (3 + √3) km D) 1/2 (√3 + 1) km 📝 Solution: 16 / 20 16. The angle of elevation of the top of a vertical tower from a point on the ground is 60° From another point 10 m vertically above the first, its angle of elevation is 45°. Find the height of the tower. A) 5 (√3 + 3) m B) 7 (√3 + 3) m, C) None of these D) 5 (√3 + 5) m, 📝 Solution: 17 / 20 17. The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled. A) True B) False 📝 Solution: 18 / 20 18. A tower 30 m high is viewed from foot of another tower, elevation = 60°, from opposite view = 30°. Find distance between towers. A) 7√3 m B) 5√3 m C) 10√3/5 m D) 10√3 m 📝 Solution: 19 / 20 19. If the height of a tower and the distance of the point of observation from its foot, both.are increased by 10%, then the angle of elevation of its top remains unchanged. A) False B) True 📝 Solution: 20 / 20 20. A man on a platform 3 m high observes a cloud at elevation θ and its reflection at depression θ. Then height of cloud is: A) Not 3 m; requires trigonometry B) h C) 3 m D) 2 × h 📝 Solution: Your score isShare Your Score with Friends Facebook Twitter 0% Send feedback
