Problems on Height and Distance

Problems on Height and Distance

Learn and practice Problems on height and distance with easy explaination and shortcut tricks. All questions and answers on height and distance covered for various Competitive Exams

Solve Problems:

1) Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse observed from the ships are 30° and 45° respectively. If the lighthouse is 100m high, find the distance between the two ships.

  1. 155.80 m
  2. 157.80 m
  3. 159. 80 m
  4. 161.80 m
View Answer

The Correctoption is(B)

Answer with explanation:

Let AB be the height of lighthouse and C and D be the positions of the ships.

AB = 100 meters, ∠ACB = 45°, ∠ADB = 60°

AC = AB (100m)

AC = 100 m

Distance between ships, CD = AC + AD

2) A ladder is leaning against a wall. It makes a 60° angle with the wall. If the distance between foot of ladder and wall is 5.5 meters, find the length of the ladder.

  1. 9.5m
  2. 10m
  3. 10.5m
  4. 11m
View Answer

The Correctoption is(D)

Answer with explanation:

Let BC be the wall and AC be the ladder.

∠BAC = 60° and AB = 5.5 meter

AC = 2 * AB

= 2 * 5.5 = 11 meters (Option D)

3) A man 1.5 meter tall is 30√3 meter away from a building. When he sees the top of building the angle of elevation is 30°. Find the height of the building?

  1. 31.5m
  2. 30 m
  3. 53.4m
  4. 48 m
View Answer

The Correctoption is(A)

Answer with explanation:

Let AD be the man and BE the building.

Now draw a line DC so that DC is perpendicular to BE.

Now, BC = AD = 1.5 m

And, DC = AB = 30√3 m

Now, Height of building, BE = BC + EC

= 1.5 + 30 = 31.5 m (Option A)

4) The angle of elevation of the top of a tower at a point X is 30°. On walking 30 m towards the tower if the angle of elevation becomes 60° at point Y, find the height of the tower?

  1. 26 m
  2. 28 m
  3. 29 m
  4. 30 m
View Answer

The Correctoption is(A)

Answer with explanation:

Let AB be the height of tower and XA be the distance between point X and base of tower.

XA = 3XA – 90

– 2XA = – 90

XA = 90/2 =45

Put the value of XA in equation (1) to find AB (height of tower).

5) The tops of two poles are connected by a wire. The heights of the poles are 10 m and 14 m respectively. If the wire makes a 30° angle with the horizontal, find the length of the wire?

  1. 7 m
  2. 7.5m
  3. 8m
  4. 8.5m
View Answer

The Correctoption is(C)

Answer with explanation:

Let AD and BE, be the poles of height 10 m and 14 m respectively.

DE is the wire of length = L

DC is parallel to AB so AD = BC = 10 m

So, CE = BE – BC = 14 – 10 = 4 m

Try to solve more problems on height and distance.

6) The angle of elevation of the sun when the length of the shadow of a pole is equal to the height of the pole is?

  1. 45°
  2. 30°
  3. 60°
  4. 90°
View Answer

The Correctoption is(A)

Answer with explanation:

Let ∠BAC = θ

Let height of pole is h and length of the shadow is L.

As per question L = h

tan θ = 1

So, when tan θ is equal to 1 the angle will be 45° (Option A)

7) A man sees the top of a tower from a point P. It makes an angle of elevation of 30° with the man’s eyes. If the height of the tower is 100 m, find the distance between man and tower?

  1. 57.8 m
  2. 110 m
  3. 173 m
  4. 140 m
View Answer

The Correctoption is(C)

Answer with explanation:

PQ = 100 * √3

PQ = 100 * 1.73

= 173 m (Option C)

8) A storm breaks a tree. The broken part of tree bends so that the top of the tree touches the ground and makes an angle of 60° with the horizontal plane. If the distance between the base of the tree and the point where top of tree touches the ground is 10 m, find the height of the tree?

  1. 37.3 m
  2. 17.3 m
  3. 27.3 m
  4. 20.3 m
View Answer

The Correctoption is(A)

Answer with explanation:

PQ = 10 and let RQ be X.

X = 10 √3

Now, PR2 = X2 + (10)2

PR2 = (10 √3)2 + (10)2

= 300 + 100

PR2 = 400

PR = 20

Height of tree = RQ + PR

= X + 20

= 10 √3 + 20

= 10 * 1.73 + 20

= 17.3 + 20

= 37.3 meter (Option A)

Try to solve more problems on height and distance.

9) The angle of elevation of the top of an unfinished building at point P which is 120 m away from its base is 30°. If the angle of elevation of the finished building at the same point would be 60°, find the height of the remaining part of the building.

  1. 70 √3 m
  2. 75 √3 m
  3. 80 √3 m
  4. 85 √3 m
View Answer

The Correct option is(C)

Answer with explanation:

Let the height of remaining part of building be X.

then,

120 + √3 X = 120*3

120 + √3 X = 360

√3 X = 360 – 120

√3 X = 240

10) The top of a 30 m high wall makes an angle of elevation of 60° with the top of a tower and makes an angle of depression of 45° with the bottom of the tower. Find the distance between tower and wall?

  1. 27 m
  2. 28 m
  3. 29 m
  4. 30 m
View Answer

The Correctoption is(D)

Answer with explanation:

Let AD is the wall of height 30 m and BE is the tower and X be the distance between tower and wall.

X = 30 m (Option D)

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