Height And Distance - Aptitude MCQ Questions and Solutions with Explanations Page-8 section-1

71.
A flagstaff is placed on top of a building. The flagstaff and building subtend equal angles at a point on level ground which is 200 m away from the foot of the building. If the height of the flagstaff is 50 m and the height of the building is h, which of the following is true?

A. h³ - 50h² + (200)²h + (200)²50 = 0

B. h³ - 50h² - (200)²h + (200)²50 = 0

C. h³ + 50h² + (200)²h - (200)²50 = 0

D. None of these

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72.
From the top of a hill 100 m high, the angles of depression of the top and bottom of a pole are 30° and 60° respectively. What is the height of the pole?

A. 52 m

B. 50 m

C. 66.67 m

D. 33.33 m

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73.
A poster is on top of a building. Rajesh is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30° respectively. What is the height of the poster?

A. $$\frac{{50}}{{\sqrt 3 }}\left( {\sqrt 3 - 1} \right)$$

B. $$50\sqrt 3 \,{\text{m}}$$

C. $$\frac{{50}}{{\sqrt 3 }}$$

D. None of these

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74.
Angles of elevation of pole are 60° and 45° from points at distances m and n on ground respectively. Here m, when measured from base of pole is less than n. What is the height of the pole?

A. $$\sqrt {mn\sqrt 3 } \,{\text{units}}$$

B. $$\sqrt {mn\root 4 \of 3 } \,{\text{units}}$$

C. $$\sqrt {3mn} \,{\text{units}}$$

D. $$\sqrt {mn} \,{\text{units}}$$

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75.
A tree is cut partially and made to fall on ground. The tree however does not fall completely and is still attached to its cut part. The tree top touches the ground at a point 10m from foot of the tree making an angle of 30°. What is the length of the tree?

A. $$10\sqrt 3 \,{\text{m}}$$

B. $$\frac{{10}}{{\sqrt 3 }}\,{\text{m}}$$

C. $$\frac{{\left( {\sqrt 2 - 1} \right)}}{{10}}\,{\text{m}}$$

D. $$\frac{{10}}{{\sqrt 2 }}\,{\text{m}}$$

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76.
Tree top’s angle of elevation is 30° from a point on ground, 300m away the tree. When the tree grew up its angle of elevation became 60° from the same point. How much did the tree grow?

A. $$100\sqrt 3 \,{\text{m}}$$

B. $${\text{200}}\sqrt 3 \,{\text{m}}$$

C. $$300\frac{1}{{\sqrt 3 }}\,{\text{m}}$$

D. $$\frac{{200}}{{\sqrt 3 }}\,{\text{m}}$$

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77.
Mohan looks at a tree top and the angle made is 45°. He moves 10 cm back and again looks at the tree top but this time angle made is 30°. How high is the tree top from ground?

A. $$\frac{{10}}{{\sqrt 3 + 1}}\,{\text{cm}}$$

B. $$20\sqrt 3 \,{\text{cm}}$$

C. $$20\,{\text{cm}}$$

D. $$\frac{{10}}{{\sqrt 3 - 1}}\,{\text{cm}}$$

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78.
Rohit while seeing a bird on tree top made 45° angle of elevation. He walks 240ft. towards the tree to observe the bird closely, thus making 60° angle of elevation. How far was Rohit from the tree initially?

A. $$\frac{{240\sqrt 3 }}{{\sqrt 3 - 1}}\,{\text{ft}}$$

B. $$\frac{{240}}{{\sqrt 3 - 1}}\,{\text{ft}}$$

C. $$\frac{{240}}{{\sqrt 3 }}\,{\text{ft}}$$

D. $$240\sqrt 3 \,{\text{ft}}$$

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79.
A tree breaks and falls to the ground such that its upper part is still partially attached to its stem. At what height did it break, if the original height of the tree was 24 cm and it makes an angle of 30° with the ground?

A. 12 cm

B. 8 cm

C. 9.5 cm

D. 7.5 cm

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80.
Two houses are in front of each other. Both have chimneys on their top. The line joining the chimneys makes an angle of 45° with the ground. How far are the houses from each other if one house is 25m and other is 10m in height?

A. 18 m

B. 12 m

C. 7.5 m

D. 15 m

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Height And Distance - Aptitude MCQ Questions and Solutions with Explanations

71. A flagstaff is placed on top of a building. The flagstaff and building subtend equal angles at a point on level ground which is 200 m away from the foot of the building. If the height of the flagstaff is 50 m and the height of the building is h, which of the following is true?

Answer & Solution

72. From the top of a hill 100 m high, the angles of depression of the top and bottom of a pole are 30° and 60° respectively. What is the height of the pole?

Answer & Solution

73. A poster is on top of a building. Rajesh is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30° respectively. What is the height of the poster?

Answer & Solution

74. Angles of elevation of pole are 60° and 45° from points at distances m and n on ground respectively. Here m, when measured from base of pole is less than n. What is the height of the pole?

Answer & Solution

75. A tree is cut partially and made to fall on ground. The tree however does not fall completely and is still attached to its cut part. The tree top touches the ground at a point 10m from foot of the tree making an angle of 30°. What is the length of the tree?

Answer & Solution

76. Tree top’s angle of elevation is 30° from a point on ground, 300m away the tree. When the tree grew up its angle of elevation became 60° from the same point. How much did the tree grow?

Answer & Solution

77. Mohan looks at a tree top and the angle made is 45°. He moves 10 cm back and again looks at the tree top but this time angle made is 30°. How high is the tree top from ground?

Answer & Solution

78. Rohit while seeing a bird on tree top made 45° angle of elevation. He walks 240ft. towards the tree to observe the bird closely, thus making 60° angle of elevation. How far was Rohit from the tree initially?

Answer & Solution

79. A tree breaks and falls to the ground such that its upper part is still partially attached to its stem. At what height did it break, if the original height of the tree was 24 cm and it makes an angle of 30° with the ground?

Answer & Solution

80. Two houses are in front of each other. Both have chimneys on their top. The line joining the chimneys makes an angle of 45° with the ground. How far are the houses from each other if one house is 25m and other is 10m in height?

Answer & Solution

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71.
A flagstaff is placed on top of a building. The flagstaff and building subtend equal angles at a point on level ground which is 200 m away from the foot of the building. If the height of the flagstaff is 50 m and the height of the building is h, which of the following is true?

72.
From the top of a hill 100 m high, the angles of depression of the top and bottom of a pole are 30° and 60° respectively. What is the height of the pole?

73.
A poster is on top of a building. Rajesh is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30° respectively. What is the height of the poster?

74.
Angles of elevation of pole are 60° and 45° from points at distances m and n on ground respectively. Here m, when measured from base of pole is less than n. What is the height of the pole?

75.
A tree is cut partially and made to fall on ground. The tree however does not fall completely and is still attached to its cut part. The tree top touches the ground at a point 10m from foot of the tree making an angle of 30°. What is the length of the tree?

76.
Tree top’s angle of elevation is 30° from a point on ground, 300m away the tree. When the tree grew up its angle of elevation became 60° from the same point. How much did the tree grow?

77.
Mohan looks at a tree top and the angle made is 45°. He moves 10 cm back and again looks at the tree top but this time angle made is 30°. How high is the tree top from ground?

78.
Rohit while seeing a bird on tree top made 45° angle of elevation. He walks 240ft. towards the tree to observe the bird closely, thus making 60° angle of elevation. How far was Rohit from the tree initially?

79.
A tree breaks and falls to the ground such that its upper part is still partially attached to its stem. At what height did it break, if the original height of the tree was 24 cm and it makes an angle of 30° with the ground?

80.
Two houses are in front of each other. Both have chimneys on their top. The line joining the chimneys makes an angle of 45° with the ground. How far are the houses from each other if one house is 25m and other is 10m in height?