## Introduction: 1 Building 2 Angles

Continuing in the series of “Trigonometry –>Height and Distance–> Five types of Questions. 4th type of question is “One buildings and Two angles”.

Such question usually revolve around 2 points on ground, 2 shadows, or flag+building or statue + building type of diagram.

Here are example questions (all of them solved in the video)

- From point A on ground, angle of elevation is 30 degree to the top of a building. Moving 20m towards the building, there is point B, with angle 60. Find height of this building
- As Sun’s angle of elevation increases from 30 to 60, shadow of a tree decreases by 5m. Find height of this tree.
- Height of a building is “h”. From a ground-point, the angle of elevation of the top of this building is “A”. On moving h/2 distance towards the building, angle becomes “B”. Find value of cotA-cotB. (
**SSC-CGL 2012**)

## Approach: 1 building 2 angles

- Since two angles are given, you make two equations of TAN using
*Topi-triangle shortcut*^{TM}. - First equation will give you a value (either height or distance). You plug that into second equation 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

- As angle of elevation of the sun increases from 30° to 60°: Shadow of the tree is reduced by 10 m find the height of this tree.
- A hill is 200 high. A car makes 30 degree angle of elevation and a truck makes 60 degree angle of elevation with this hill. Find distance between these two vehicle. (hint: 30<60 so car will be farther away from hill compared to truck.)
- There is a palm tree on the bank of a river. A person is observing this tree from the opposite bank. Angle of elevation is 60. Now he retreats (moves back) 20 meters from his side of bank. And the angle of elevation is decreased to 30. Find 1) height of tree 2) width of river.
- Two buildings of same height are located on the either side of a road. width of the road is hundred metres. At a point on the road, between these two buildings, the angle of elevation for each building are 60 and 30 m respectively. Find the distance of the point from the nearest end of a building and find the height of these buildings.
- A statute is 1.46 m tall. And it stands on the top of a pedestal. From a ground point, angle of evaluation of elevation of the statue is 60° and from the same ground point, the angle of elevation of the top of the pedestal is 45°. Final height of the pedestal. (hint: TAN 45=opposite and adjacent sides are same)
- Angles of elevation of a building from two points at distance of A and B (A>B) from its foot on the same side of building have measure 30 and 60. Find height of tower.
- From the top of a lighthouse, two ships “A” and “B” are visible on the same side of the sea. If their angles of depression are 35 and 50 degrees respectively, then which ship is farther away from the lighthouse?
- from a ground point, the angle of elevation of a building is found to be such that Tangent is 5/12. after walking 192 m towards the building, thangent changes to 3/4. find height of the building. (hint:Tangent=TAN.)

## Answers

- 5 ROOT 3 OR 8.65
- 400 root 3 by 3 OR 230.6
- Height of tree 10 root 3 or 17.3 and width of river 10.
- distance of point from the nearest building=25m. height of each building is 25 root 3 OR 43.25 m
- 2m
- root (ab)
- Ship A is farther away because its angle of elevation is 35. Smaller the angle of elevation =farther away from base.
- 3

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

Manohar N07/03/2013 at 12:34 amSir , for question 7 answer is ship B because they given angle of depression not angle of elevation

Karan08/03/2013 at 9:00 pmangle of depression from top of the bldg is measured n angle of elevation from bottom..

so ans 7 is correct!!

ship A

Jithesh09/03/2013 at 10:19 pmSir, Could you please provide the steps for the question number 8.

arun10/03/2013 at 1:48 ammrunal please shed some light on lic aao examiantion

Mrunal10/03/2013 at 9:04 pmSure but it’ll take some time. Right now busy with UPSC pattern change article.

Aiman Reyaz10/03/2013 at 9:44 pmThank you. You earn my blessings.

shailendra singh15/03/2013 at 5:41 pmsir that’s great help by U, may i get information for UGC NET HISTORY

saravanan17/03/2013 at 10:10 pmSir, Can you please upload the solution diagrams/step sequence for the mock questions 6 and 8. I was unable to understand the problem.

Natasha20/03/2013 at 9:38 amsir for question 4

i cant understand the diagram.. plz give the solution

anshu29/03/2013 at 9:45 pmsir, I am getting different answers for question 6th and 8th . for 8th answer should be 180 meters.

neha04/04/2013 at 3:35 amsame here….1 am getting 180m as 8th answer

tushar17/04/2013 at 3:57 pmquestion 8th answer is 180.

aspirant18/02/2016 at 6:46 amtotally agree with you!!!

kindly upload the steps for question 4 and 6….

sudhir07/04/2013 at 1:31 pmsir plz post about geometry and mensuration

vinod kumar09/04/2013 at 11:14 pmplz expalin question no 8

Prakash12/04/2013 at 7:34 pmMrunal Sir, Quantum Cat book by Sarvesh Verma has omitted many solutions in Trigonometry Chapter. What to do?

No solution for Introductory Exercise and for Level 1 only 15 questions solutions are there.

Can you give us links for the rest of the answers?

Also thanks for clearing the basics of Trigonometry.

Best Regards.

Lakhan Jadeja15/07/2013 at 11:19 pmplz explain 5th uska diagram kese banaya jaye samaj me nahi a raha

Ricky Bhattacharya24/07/2013 at 10:36 pmSir,

Unable to solve some of the mock questions , but those are also very important.. Where to find the solutions of those ..??

Please help sir …

Thanks in advance ..

Neeraj25/07/2013 at 1:08 pmsir please shed some light on ssc capf si exam also.

AS13/09/2013 at 8:49 pmSir, Please provide solutions for Question 6 and 8. Thanks in advance.

Imcmin30/08/2014 at 9:25 amAnswer to ques.8 should be 180.

Manu Reddy05/09/2014 at 8:05 amCould any one please explain 8th question.