Height and Distance MCQ

Test your knowledge with important Height and Distance MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Height and Distance MCQs at Bissoy

• Due to sun, a 6ft man casts a shadow of 4ft, whereas a pole next to the man casts a shadow of 36ft. What is the height of the pole?
  ক

  63 ft

  খ

  72 ft

  গ

  54 ft

  ঘ

  48 ft
• Raj stands in a corner of his square farm. Angle of elevation of a scarecrow placed in diagonally opposite corner is 60°. He starts walking backwards in a straight line and after 80ft he realizes that angle of elevation of the scarecrow now is 30°. What is area of the field?
  ক

  1600 sq.ft.

  খ

  40 sq.ft.

  গ

  $$\frac{{40}}{{\sqrt 2 }}$$ sq.ft.

  ঘ

  800 sq.ft.
• There is a tower of 10m between two parallel roads. The angles of depression of the roads from the top of the tower are 30° and 45°. How far are the roads from each other?
  ক

  27.32 m

  খ

  29.56 m

  গ

  $$20\sqrt 3 \,{\text{m}}$$

  ঘ

  $$\frac{{10}}{{\sqrt 3 }}\,{\text{m}}$$
• A and B are standing on ground 50 meters apart. The angles of elevation for these two to the top of a tree are 60° and 30°. What is height of the tree?
  ক

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

  খ

  $$\frac{{25}}{{\sqrt 3 }}\,{\text{m}}$$

  গ

  $$25\sqrt 3 \,{\text{m}}$$

  ঘ

  $$\frac{{25}}{{\sqrt 3 - 1}}\,{\text{m}}$$
• Ramesh and Suresh’s mud forts have heights 8 cm and 15 cm. They are 24 cm apart. How far are the fort tops from each other?
  ক

  31 cm

  খ

  24 cm

  গ

  25 cm

  ঘ

  24.5 cm
• There is a tree between houses of A and B. If the tree leans on A’s House, the tree top rests on his window which is 12 m from ground. If the tree leans on B’s House, the tree top rests on his window which is 9 m from ground. If the height of the tree is 15 m, what is distance between A’s and B’s house?
  ক

  21 m

  খ

  25 m

  গ

  16 m

  ঘ

  12 m
• Shadow of a man is $$\frac{1}{{\sqrt 3 }}$$ times the height of the man. What will be the sun’s angle of elevation?
  ক

  135°

  খ

  45°

  গ

  30°

  ঘ

  60°
• 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?
  ক

  18 m

  খ

  12 m

  গ

  7.5 m

  ঘ

  15 m
• 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?
  ক

  12 cm

  খ

  8 cm

  গ

  9.5 cm

  ঘ

  7.5 cm
• 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?
  ক

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

  খ

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

  গ

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

  ঘ

  $$240\sqrt 3 \,{\text{ft}}$$
• 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?
  ক

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

  খ

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

  গ

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

  ঘ

  $$\frac{{10}}{{\sqrt 3 - 1}}\,{\text{cm}}$$
• 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?
  ক

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

  খ

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

  গ

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

  ঘ

  $$\frac{{200}}{{\sqrt 3 }}\,{\text{m}}$$
• 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?
  ক

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

  খ

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

  গ

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

  ঘ

  $$\frac{{10}}{{\sqrt 2 }}\,{\text{m}}$$
• 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?
  ক

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

  খ

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

  গ

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

  ঘ

  $$\sqrt {mn} \,{\text{units}}$$
• 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?
  ক

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

  খ

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

  গ

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

  ঘ

  None of these
• 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?
  ক

  52 m

  খ

  50 m

  গ

  66.67 m

  ঘ

  33.33 m
• 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?
  ক

  h³ - 50h² + (200)²h + (200)²50 = 0

  খ

  h³ - 50h² - (200)²h + (200)²50 = 0

  গ

  h³ + 50h² + (200)²h - (200)²50 = 0

  ঘ

  None of these
• The elevation of the summit of a mountain from its foot is 45°. After ascending 2 km towards the mountain upon an incline of 30°,the elevation changes to 60°. What is the approximate height of the mountain?
  ক

  1.2 km

  খ

  0.6 km

  গ

  1.4 km

  ঘ

  2.7 km
• From a tower of 80 m high, the angle of depression of a bus is 30°. How far is the bus from the tower?
  ক

  40 m

  খ

  138.4 m

  গ

  46.24 m

  ঘ

  160 m
• From the foot and the top of a building of height 230 m, a person observes the top of a tower with angles of elevation of b and a respectively. What is the distance between the top of these buildings if tan a = $$\frac{5}{{12}}$$ and tan b = $$\frac{4}{{5}}$$
  ক

  400 m

  খ

  250 m

  গ

  600 m

  ঘ

  650 m
• Two vertical poles are 200 m apart and the height of one is double that of the other. From the middle point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary. Find the heights of the poles.
  ক

  141 m and 282 m

  খ

  70.5 m and 141 m

  গ

  65 m and 130 m

  ঘ

  130 m and 260 m
• A man on the top of a vertical observation tower observers a car moving at a uniform speed coming directly towards it. If it takes 8 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower?
  ক

  8 min 17 second

  খ

  10 min 57 second

  গ

  14 min 34 second

  ঘ

  12 min 23 second
• Two persons are on either sides of a tower of height 50 m. The persons observers the top of the tower at an angle of elevation of 30° and 60°. If a car crosses these two persons in 10 seconds, what is the speed of the car?
  ক

  $$24\sqrt 3 \,{\text{km/hr}}$$

  খ

  $$\frac{{20\sqrt 3 }}{3}\,{\text{km/hr}}$$

  গ

  $$\frac{{24}}{{\sqrt 3 }}\,{\text{km/hr}}$$

  ঘ

  None of these
• The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree, is:
  ক

  30°

  খ

  60°

  গ

  45°

  ঘ

  None of these
• An aeroplane when 900 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 60° and 45° respectively. Approximately, how many meters higher is the one than the other?
  ক

  381 m

  খ

  169 m

  গ

  254 m

  ঘ

  211 m
• A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 100 metres from the tower. After 10 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?
  ক

  26.28 km/hr

  খ

  32.42 km/hr

  গ

  24.22 km/hr

  ঘ

  31.25 km/hr
• A vertical pole fixed to the ground is divided in the ratio 1 : 9 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, 15 m away from the base of the pole, what is the height of the pole?
  ক

  $$60\sqrt 5 \,{\text{m}}$$

  খ

  $${\text{15}}\sqrt 5 \,{\text{m}}$$

  গ

  $$15\sqrt 3 \,{\text{m}}$$

  ঘ

  $${\text{60}}\sqrt 3 \,{\text{m}}$$
• A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?
  ক

  9 units

  খ

  $$3\sqrt 3 $$ units

  গ

  Data inadequate

  ঘ

  12 units
• A ladder 10 m long just reaches the top of a wall and makes an angle of 60° with the wall.Find the distance of the foot of the ladder from the wall $$\left( {\sqrt 3 = 1.73} \right)$$
  ক

  4.32 m

  খ

  17.3 m

  গ

  5 m

  ঘ

  8.65 m
• The angle of elevation of the top of the tower from a point on the ground is $${\sin ^{ - 1}}\left({\frac{3}{5}} \right).$$   If the point of observation is 20 meters away from the foot of the tower, what is the height of the tower?
  ক

  9 m

  খ

  18 m

  গ

  15 m

  ঘ

  12 m