Important Notes & Short Tricks on Height & Distance Part -2

In this part, we will try to solve questions with the help of ratio. This trick will save a lot of time and useful during the exam period. This article also contains some useful formula.

Here are some ratio figure which you have to remember

Important short tricks are :

Note:  only when the sum of angle i.e  

Some Important questions are as follows:

Example 1:The angle of elevation of the top of a tower at a distance of 500 m from its foot is 30°. The height of the tower is :

(a)

(b)

(c)500

(d)

Ans. (d)

Short trick:

Solve it with ratio, as the angle of elevation is 30° then ratio between P: B: H  is 1:√3:2 so √3= 500 then 1= 500/√3 and height is equal to 

Example 2: The banks of a river are parallel. A swimmer starts from a point on one of the banks and swims in a straight line inclined to the bank at 45⁰ and reaches the opposite bank at a point 20 m from the point opposite to the starting point. The breadth of the river is :

(a)  20 m

(b)  28.28 m

(c)   14.14 m

(d)  40 m

Ans. (c) 14.14 m

Solution:

Let A be the starting point and B, the endpoint of the swimmer. Then AB = 20m &  

Short Method;

AS the angle of elevation is 45° then the ratio of P: B : H i.e. 1:1:√2

here √2 =20 then 1 =20/√2

Question 3: A man from the top a 50m high tower, sees a car moving towards the tower at an angle of depression of 30⁰. After some time, the angle of depression becomes 60⁰. The distance (in m) travelled by car during this time is –

(a)

(b)

(c)

(d)

Ans. (c)

Solution: 

AB = AC – BC

Example 4:A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite side of the bank is 60⁰. When he moves 50m away from the bank, the angle of elevation becomes 30⁰. The height of the tree and width of the river respectively are :

(a) 

(b)  

(c) 

(d)  None of these

Answer: c)

Solution: 

Ratio value original value

height of the tree= h (ratio value = )=

and width of the river = x (ratio value = 1) = 25 m

Example 5: From the top of a pillar of height 80 m the angle of elevation and depression of the top and bottom of another pillar are 30⁰ and 45⁰ respectively. The height of the second pillar (in metre) is:

(a)    m

(b)  

(c)    

(d) 

Answer: (c)

Solution: 

Let AB and CD are pillars.

Let DE = h

In 

Required height