# Introduction: 1 building 1 angle

Starting the series of “Trigonometry –>Height and Distance(HnD)–> Five types of Questions.
1st and most easiest of all height n distance questions is “1 building 1 angle”. Here are example questions (all solved in the video)

1. There is a temple on a river of bank. From the other side of the bank, angle of elevation is 30 degree, and height is 20m. Find the width of river
2. A kite is flying in the sky, length of thread is 150m. If the thread makes 60 degree angle of elevation , find the height @which kite is flying
3. A man is 1.5 tall. He is 28.5 m away from a building. Angle of Elevation is 45. Find height of building.

Instead of building, they can use different words like tree, telephone pole, building, tower, lighthouse,castle, mountain, hill, cliff etc. but the approach remains one and same.

# Approach: 1 building 1 angle 1. (In most cases), Just make one equation of TAN
2. Plug in the standard value of TAN angle, using Topi-trianglesTM.
3. Solve the equation.
4. That’s it, you got the answer. (in some cases, you’ll need to use SIN or COS instead of TAN).

Watch 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

1. An electrical pole is 5m long. An electrician needs to reach a point 2 meters below the top of this pole to repair the wiring. He uses a ladder, which makes an angle of elevation 60 degrees. Find the length of this ladder.
2. A pole stands vertically on the ground. From a point 90 m away from this pole, the angle of elevation is 30° find the height of this pole
3. String of a kite is 100 metres long and it makes an angle of 60° with the ground. Find the height at which the kite is flying.
4. There is a 10m high pole. A rope is attached to it and tied to a point on ground. Angle of elevation is 30. Now an acrobat starts climbing using this rope. Calculate the distance covered by artist in climbing to the top of the pole. (hint find length of hypotenuse or rope.)
5. Height of a mountain is “m” meters.  angle of elevation from the ground is 30°.  if you start walking from the bottom of the mountain and reach to the top,  how much distance have you covered? (hint: he is asking about Hypotenuse. Use SIN 30)
6. From a point on ground, the Angle of elevation of the top of a tower is 45 degrees.  if the height of the tower is “A” and  the distance between ground point and bottom of tower is “B”.  then find relationship between “A” and “B”. (equal/ greater than/less than).
7. A 3 m long ladder leans on a wall, such that its lower end remains 1.5 m away from the Base of the wall.  find the angle of elevation. (hint match COS value)
8. A building is 50 root 3m tall. For a point on ground that is 50m away from the building, find angle of elevation
9. Ratio of length of a building and its shadow is 1: root 3. Find angle of elevation of the sun.
10. From a ground point that is 400 meters away from a building, the angle of elevation is 30 degrees. Find height of this building
11. A ship is “a” meters away from the bottom of a 30 meter tall lighthouse. The angle of elevation is 60 degrees. Find the value of “a”.
12. What is the angle of elevation of Sun, if the length of a tree and its shadow are same? (hint: find TAN degree where opposite and adjacent sides are same!)

1. 2 root 3 or 3.46
2. 51.9
3. 50 root 3 OR 86.5
4. 20
5. 2m
6. Equal because 45. And tan45=1
7. 60 degrees
8. 60
9. 30
10. 400 by root 3.
11. 10 root 3
12. 45

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

## Mrunal recommends

Books: UPSC Prelims Books: UPSC Mains Books: Maths /Reasoning

## 16 Comments on “[Trigonometry] HnD Type #1: One Building One Angle finding height, distance or hypotenuse”

1. God bless You Mrunal.

2. mrunal sir plz guide about new syllabus

3. thanuk sir..

4. thanks sir……… trigonometry is headache for me…….. but now its fun..

5. sir plz explain mock ques 11

7. @vivek and @vaishu- For question number 11..
perpendicular=30m
base=a meter
and angle of elevation from ground is 60

so

tan theta= p/b
tan 60=30/a
root 3=30/a
a=30/root 3

a=10 root 3

8. Plz explain 8

9. sir to point out, is the answer of que-2 is 51.9 or 52.02

10. sorry to point out about the answer of question no.-2 of the mock test.

11. sir according to your short trick for finding trignomectric ratios of cos, sin,tan 30,60,45 degree in youtube video, the value of sin 30 is root 3 by 2 but the actual value is 1 by 2(ie 1/2). and so is for sin 60,cos 30, cos 60 angles.

i think there is huge mistake in it…and the value of 30 and 60 degreee angle may br reveresed mistaknly..
please clarrify me if i am wrong

1. got the answer sir…actually it was my mistake. i took value of sin thetha = adjusant/ hypotn. rather than taking it as sin thetha= opposite/hypotn.

12. Sir can u plzz help me to solve the below question??

A house 15 metres high stands on one side of a park and from a point on the roof of the house, the angle of depression of the foot of a chimney is 30 degree and the angle of elevation of the top of the chimney from the foot of the house is 60 degree. what is the height of the chimney? what is the distance between the house and the chimney?

1. if angle of depression from house is 30degree, then angle of elevation from foot of the chimney will be 60degree…
Now,
to find distance between house:-
tan 60= height of house/distance between house and chimney(x)
=> 1/root3=15/x
=>x=15root3… this is distance between them

now,
to find height of chimney:-
Tan60=height of chimney(y)/distance between house and chimney(x)
=>root3=y/15root3
=>y=root3*15root3
=>y=45… this is height of chimney.

13. ,,thank u very much sirr..

14. Sir help me to solve this question. An Electrician pylon stands on level ground. At a point 125m from the foot of the pylon the angle of elevation of the top of the pylon is 34 degrees. Find the height of the pylon and the angle of elevation of its mid-point of its height?