Aptitude - Height and Distance - Discussion

Discussion :: Height and Distance - General Questions (Q.No.1)

1. 

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

[A]. 173 m
[B]. 200 m
[C]. 273 m
[D]. 300 m

Answer: Option C

Explanation:

Let AB be the lighthouse and C and D be the positions of the ships.

Then, AB = 100 m, ACB = 30° and ADB = 45°.

AB = tan 30° = 1         AC = AB x 3 = 1003 m.
AC 3

AB = tan 45° = 1         AD = AB = 100 m.
AD

CD = (AC + AD) = (1003 + 100) m
= 100(3 + 1)
= (100 x 2.73) m
= 273 m.


Sunitha said: (Nov 15, 2010)  
How to find out root 3?

Ravi said: (Dec 15, 2010)  
Why we take AB/AC, AB/AD?

Sam said: (Jan 25, 2011)  
Just remember root3=1.73 and root2=1.41

we take ab/ac because we want to find ac and we only know ab thats it

Srikanth said: (Feb 5, 2011)  
Why you taken Tan and why you not taken cos ?

Jowy said: (Feb 22, 2011)  
The tan30 is root(3) divide by 3. So how did you get root(3) ?

Mouli said: (Mar 17, 2011)  
I am not understand jowy said.

M.V.Krishna said: (Apr 6, 2011)  
From the figure shown above

sin30=(BA/BC); sin45=(BA/BD)

=> (1/2)=(100/BC); =>(0.7071)=(100/BD)

=>BC=200m; =>BD=141.42

by pythagorean theorem:

in a rt. angled triangle, the sum of squares of the two sides

(smaller sides) of a triangle is equal to the square of third

side(larger side).

in triangle BCA

(BC)^2 = (BA)^2 +(AC)^2

(200)^2=(100)^2+(AC)^2

=>AC=173.2m

in triangle BDA

(BD)^2 = (BA)^2 +(AD)^2

(141.42)^2=(100)^2+(AC)^2

=>AC=100m

Distance between two boats=AC+AD

=>173m+100m = 273m

Krishna said: (Jun 14, 2011)  
Why we used Tan please clarify ?

Periyasamy said: (Jun 22, 2011)  
Can you please give us notes of trignometric formulas which are used to solve height and length problems?

Ankit said: (Aug 11, 2011)  
Why you taken Tan and why you not taken cos ?

Bhupal said: (Sep 6, 2011)  
From triangle bca we know only value of ba & bca cone and we find ac i.e. base from trigonmetric formula tan is best because tan=vertical/base.

Bhupal said: (Sep 6, 2011)  
From triangle bca we know only value of ba & bca cone and we find ac i.e. base from trigonmetric formula tan is best because tan=vertical/base.

Bhupal said: (Sep 6, 2011)  
From triangle bca we know only value of ba & bca cone and we find ac i.e. base from trigonmetric formula tan is best because tan=vertical/base.

Dharani said: (Oct 21, 2011)  
tan is because sin/cos.

Sanjana said: (Nov 25, 2011)  
We can find square roots of any numbers by a special type of division or a method known as column method.

Anish Kumar said: (Jan 11, 2012)  
We can also able to find the answer using sin and cos. But more step is needed.

Sahil said: (Feb 9, 2012)  
How to calculate (root 3 + 1) manually, is there any way ?

Shro said: (Feb 20, 2012)  
@Sahil
square root of 3 is 1.73.
So ,add 1.73 + 1 = 2.73

Ram said: (Mar 11, 2013)  
How can you write AD=AB?

Pradeep K Kerketta said: (Oct 26, 2013)  
How can you manually calculate root 3?

Sumedha said: (Aug 8, 2014)  
Why we have taken tan and not sin and cos?

Manisha said: (Aug 13, 2014)  
Why we taken only tan? please explain.

Srinureddy said: (Aug 18, 2014)  
Hello friends. As best of my knowledge. Here we find the distance between two ships i.e. (AC+AD).

Here we know the height of the lighthouse (AB=100m). For the sake of we taken only (TAN = AB/AC). But not take. Sin&Cos.

Prasad said: (Dec 10, 2014)  
How to solve the problem I am not under standing for Tan value.

Vijeth said: (Aug 22, 2015)  
Why you multiply 3?

Bhanu said: (Aug 26, 2015)  
Section A of 5th standard has a class strength of 40 with an average height of 100.5 cm. Section B has a class.

Strength of 50 with an average height of 96 cm. What is the weighted average height of students in the 5th.

Standard? (Rounded to the nearest 0.5 cm).

Ganesh said: (Sep 28, 2015)  
Just try to understand.

We need to find AC and we know only AB.

BY P. Theorem, perpendicular/base, i.e.. AB/AC i.e., = tan.

1) We didn't know the value CB, if we take AB/CB no AC omit this.

2) AC/CB both value not known so no chance.

3) There is nothing called AC/AB mean base/perpendicular cancel this.

That's it try to read formula section you will understand.

Siddhant Acharya said: (Dec 30, 2015)  
It has been asked the distance between the two ships not the distance between the peak of the lighthouse and the ship. The one which has an elevation of 30 degrees will have a different value rather than (100 root 3).

Anjum Shaikh said: (Jan 1, 2016)  
Can you give me trigonometry formula which are use to solve height and length of problem?

How can we solve problem in less time logically?

Dinesh Rana said: (Feb 9, 2016)  
Simply we can easily solve the problem.

We can use the trigonometric formula:

As we know that:

(1) sinx = perpendicular/hypotenuse.

(2) cosx = base/hypotenuse and third one is a.

(3) tanx = perpendicular/base.

P.Dhana Lakshmi said: (Jul 22, 2016)  
Nice explanations, Thank you all.

Akash Rai said: (Jul 27, 2016)  
Then, AB = 100 m, ACB = 30° and ADB = 45°.

AB = tan 30° = 1, AC = AB x 3 = 1003 m.
AC = 1003 m.
AB = tan 45° = 1, AD = AB = 100 m.
AD
CD = (AC + AD) = (1003 + 100) m.
= 100(3 + 1).
= (100 x 2.73) m.
= 273 m.

That Proved.

Kavya Sreeram said: (Aug 18, 2016)  
Tan 30 is 1/√3 right? then in all problem, it is 1, how come?

Radhika Mane said: (Aug 22, 2016)  
How to take root 3 value?

Ram said: (Oct 4, 2016)  
I do not understand. Please, anyone, give a simple explanation.

Akhilesh Agrahari said: (Oct 12, 2016)  
By taking 100 common in 100 and 100root3.

Sandy said: (Oct 20, 2016)  
How to take root 3? Please explain.

Babu said: (Oct 27, 2016)  
What do mean by sailing?

Imtiyaz said: (Jan 10, 2017)  
How to find the root of 3?

Pranso said: (Jan 24, 2017)  
Great explanation, thank you so much for all your answers.

Rohit said: (Mar 7, 2017)  
I don't understand the answer. Please anyone help me to get it.

Abijith said: (Mar 11, 2017)  
What is root 3 value?

Vino said: (Mar 28, 2017)  
The value of √ 3 is 1.732.

Mani said: (Apr 25, 2017)  
How can you take √3 is 1.732? Can anyone explain?

Masthan Shaik said: (May 6, 2017)  
√3 means the square of 3.

It calculated as 1.732. Because two same numbers give their square root.
i;e 2 * 2 = 4,3 * 3 = 9 just like this 1.732 * 1.732 = 2.999824 it is nearest to 3 then 1.732 is square root of 3.

Gaurav Radheshyam Jaiswal said: (Jun 17, 2017)  
Why are used tan only?

Amol Meher said: (Jun 19, 2017)  
Why are uesd tan? Please explain me.

Preetam said: (Jul 5, 2017)  
We have taken tan. Instead of sin or cos because perpendicular is given and we need to find the base, so tan is equal to perpendicular/base. So for that, we need a tan.

Swapnil said: (Jul 9, 2017)  
How to find root3 value, please explain in detail. How to come 1.732?

Kumar said: (Jul 24, 2017)  
How can you get AB/AC=tan 30*=1/√ 3?

Sathish said: (Sep 13, 2017)  
Why we have use tan?

Jeni said: (Sep 17, 2017)  
How the value of AD is said to be 100?, It is not given question, but it is said to be 100? why?

Sathish said: (Sep 21, 2017)  
Why we use tan instead of cos, sin please explain?

Sehdev said: (Sep 25, 2017)  
How we calculated the square root of 3 that we got 1.73?

Kushal Neupane said: (Oct 4, 2017)  
How we calculated the square root of 3 that wu got 1.73?

Soraj said: (Oct 8, 2017)  
How to proved AB*3=1003?

we know AB Is 100,
So I put the AB*3=100*3=300,
But why this is 1003.

Kolleru Saikumar said: (Oct 21, 2017)  
The distance between 2 ships equal to 273 meters.

Amit M said: (Jan 4, 2018)  
Is there any other solutions that sin cos tan?

Yash said: (Jan 9, 2018)  
We can find AD, IF we use Tan then only we find AD. So we use tan. By using sin and cos also we can solve.

Darshan said: (Mar 7, 2018)  
How will we get root3 = 1.73?

Mari said: (Mar 10, 2018)  
The value of √3 is 1.732.

Manu said: (May 30, 2018)  
Why we are using tan instead of cos, can explain that?

Dileep said: (Jun 14, 2018)  
Why we to have use tan?

Shubham said: (Jun 18, 2018)  
Tan = perpendicular/Base, the value of perpendicular has been given and we have to find the base, that's why the tan is used.

Mky said: (Jul 2, 2018)  
Why we using only tan why not cot, sin, cos?

Akshay said: (Jul 25, 2018)  
Why two sides ac and ad are taken as opposite sides in a lighthouse although it is not given we can take another side also if we think in 3D?

Rushikesh said: (Aug 18, 2018)  
How to find out the 100 * √3?

Ramya said: (Sep 3, 2018)  
Please explain me the solution clearly.

Mano said: (Sep 11, 2018)  
Why using tan here?

Yogita Sable said: (Oct 8, 2018)  
I am not getting it. Please explain in details.

Uttam Singh said: (Oct 9, 2018)  
We can use a Divide rule to find the root of any number.

Naveen said: (Jan 5, 2019)  
Why should we take tan? Anyone explain me.

Naveen said: (Jan 5, 2019)  
Why should we take tan? Anyone explain me.

Garalapati Bharadwaja said: (Jan 8, 2019)  
Why should we take only tan? Anyone explain me.

Kishor said: (Jan 8, 2019)  
How? tan 45° = 1
AD = AB = 100 m. How it is? Explain in detail.

Kowsalyadevi said: (Mar 28, 2019)  
First, understand the problem from the given Diagram.

We have to find the distance of the CD.
So, first identify how to use 45° and 35°.
Only by using tan because we know AB value
We know that tanx = perpendicular/base.

tan 30° = AB/CA.
1/√3= 100/CA.
CA=100 x √3.
tan 45° = AB/AD.
1 = 100/AD,
AD = 100.
We know that CD = CA+CD.
= 100x√ 3+100,
= 100(√3+1),
= 100(1.73+1),
= 100(2.73),
= 273m.

Divakar said: (Apr 20, 2019)  
What is the reason to take tan? Please tell me.

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