## Introduction: 2 Building 2 Angles

Continuing in the series of “Trigonometry –>Height and Distance–> Five types of Questions.

4^{th} type of question is “Two buildings and Two angles”. Here are example questions (both solved in the video)

- From the bottom of a 50m temple, the angle of elevation of the top of next building is 60. Similarly, from the bottom of the building, angle of elevation of the top of the temple is 30 degree. Find height of this building.
- From the top of a 90m cliff, angle of depression of top and bottom of a building are 30 and 60 degrees respectively. Find height of this building
**(SSC CGL 2012)**

## Approach

- Since two angles are given, you make two equations of TAN using
*Topi-triangle shortcut*^{TM}. - Then combine the concept of rectangle (opposite sides have same length) And you’ll get the answer.
- Check the following video to see how ^this approach exactly works. And after watching the video, solve the mock questions given at the bottom of this article.

If the video is not visible, check it directly on my youtube channel youtube.com/user/TheMrunalPatel

## Mock Questions: 2 Building, 2 Angles

- From a 60 m tall building, the angle of depression of the top and the bottom of a tower is 30 and 60° respectively. Find the height of this tower.
- From the top half a 300 m high cliff, the angles of depression of the bottom and top of a building are 60 and 30 respectively. Find the height of this building
- watching from a window 40m high of a multi-storey building, the angle of elevation of the top of a tower is found to be 45°. The angle of elevation of the top of the same tower from the bottom of this building is 60 degrees. Find height of tower
- from the top of a 60m tall building, the angle of depression of top and bottom of a tree are 30 and 60° respectively. 1) find the distance between building and tree.2) find height of the tree. 3) find the difference between the heights of trees and building.
- The top of two buildings of height 18m and 12m are connected by a cable. This cable makes an angle of 30 meter with the horizontal line passing from the top of the smaller building. Find length of the wire.
- The angle of elevation of top of building A from bottom of building B is 50 degrees. The angle of elevation of top of building B from bottom of Building A is 70 degrees. Find out which building is taller?(hint: no calculation needed, just common sense).

## Answers

- 40
- 200
- 94.6
- 1) distance= 20 root 3 OR 34.6m 2) height of tree= 40 m 3) difference between heights= 20 m.
- 12m
- Building B is taller. (because second angle is 70 means from the bottom of building A, you’ve to raise you head even higher to see the top of building B.)

For more [Aptitude] related content, visit the Archive on Mrunal.org/aptitude

## 12 Comments on “[Trigonometry] HnD Type #4: Two Buildings-Two Angles made easy for SSC”

Thank u…:)

very much helpful

mrunal bhai excellent

woe… awesome.. 1st time a saw you…

clear and lucid language .. very much helpful to SSC aspirants..you are doing a very commendable job.

sir, I am soumika. I am a post graduate in maths. sir, am I eligible to apply for ssc stenographar exam? If any special course is required for this exam, please tell me.

sir cn u please chck the answr of qustn 5..i thnk its 6 root 3

no its 12..

sin 30 value we have to take.

here small building is given 12 and big building is given 18 and angle of elevation is given 30′

so 18-12=6m

big building is bigger than small building by 6 m

now take a sin30=opposite/hypotenuse

so 1/2=6/hypotenuse

ans is 12m

can anyone help me to find out the ans of question no. 3

two towers in front of each other (one shorter one longer)

One’s height is 40 other is 40+x

Let the distance between both towers is ‘d’

angle of Elevation from Shorter tower to the longer one is 45.

so, Tan 45 = x /d

=> x = d

Now , Angle of Elevation from bottom of shorter tower to top of longer on is 60.

Tan 60 = (x+40) /d

Sqrroot 3 = (x+40) / x (since x =d)

1.73x-x =40

x=40/0.73 = 54.5 (approx u can calculat if u want)

now its asking the height of longer tower which is x + 40 add = 55 + 40 = 94.5

The figure is given in the video at 5:00

Take the same figure and put the values .

Instead of h its 40 , instead of 90 = x + 40

upper angle is 45 , lower angle is 60

Question no 4 ans should be 4.1) distance= 15 root 3 OR 34.6m 2) height of tree= 45 m 3) difference between heights= 30 m.

answer to 2nd question shud be 100

can anyone help??

All the answers given are correct, kindly look out for your mistakes.

Can anyone please explain me answer for ques 2.. I get 100 as answer..