## 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

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