Height and Distance formulas with examples for SSC and Bank Exams

Height and Distance Formulas with Examples for Competitive Exams

Ex.6. If the height of a pole is 2√3 metres and the length of its shadow is 2 metres, the angel of elevation of the sun.

Let AB be the pole and AC be its shadow.

Let angle of elevation, ∠ABC = θ.

Then, AB = 2√3 m, AC = 2 m.

So, the angel of elevation is 60⁰

Ex.7. A ladder leaning against a wall makes an angle of 60⁰ with the ground. If the length of the ladder is 19 m, find the distance of the foot of the ladder from the wall.

Let AB be the wall and BC be the ladder.

Then, ∠ABC = 60⁰ and BC = 19 m.

Let AC = x metres

∴ Distance of the root of the ladder from the wall = 9.5

Ex.8. The angle of elevation of the top of a tower at a point on the ground is 30⁰ On walking 24 m towards the tower, the angle of elevation becomes 60⁰. Find the height of the tower.

Let AB be the tower and C and D be the points of observation. Then,

  Hence, the height of the tower is 20.76 m.

Ex.9. A man standing on the bank of a river observes that the angle subtended by tree on the opposite bank is 60⁰ When he retries 36 m from the bank, he finds the angle to be 30⁰. Find the breadth of the river. Find the breadth of the river.

Let AB be the tree and AC be the river. Let C and D be the two position of the man. Then,

Then, ∠ABC = 60⁰, ∠ADB=30⁰  and CD = 36.

Let AB = h metres and AC = x metres.

Then, AD = (36+x) metres.

  From (i) and (ii), we get :

So, the breadth of the river = 18 m.

Ex.10. A man on the top of a tower, standing on the seashore finds that a boat coming towards him takes 10 minutes for the angle of depression to change from 30⁰ to 60⁰. Find the time taken by the boat to reach the shore from this position.

Let AB be the tower and C and D be the two positions of the boat.

Let AB = h, CD = x and AD = Y.

  Hence, required time = 5 minutes

I hope these formulas will helpful for your score high. You can ask me anything in the comment section related height and distance formulas with examples.