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# Aptitude - Height and Distance - Discussion

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"Success has many fathers, while failure is an orphan."
- (Proverb)
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 30º and 45º 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

Explanation:

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

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

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

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

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

 Sunitha said: (Mon, Nov 15, 2010 08:22:41 PM) How to find out root 3?

 Ravi said: (Wed, Dec 15, 2010 07:03:43 AM) Why we take AB/AC, AB/AD?

 Sam said: (Tue, Jan 25, 2011 07:14:58 AM) 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: (Sat, Feb 5, 2011 09:06:03 PM) Why you taken Tan and why you not taken cos ?

 Jowy said: (Tue, Feb 22, 2011 09:03:10 AM) The tan30 is root(3) divide by 3. So how did you get root(3) ?

 Mouli said: (Thu, Mar 17, 2011 06:07:36 AM) I am not understand jowy said.

 M.V.Krishna said: (Wed, Apr 6, 2011 10:33:32 PM) 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: (Tue, Jun 14, 2011 10:01:45 PM) Why we used Tan please clarify ?

 Periyasamy said: (Wed, Jun 22, 2011 03:28:45 PM) Can you please give us notes of trignometric formulas which are used to solve height and length problems?

 Ankit said: (Thu, Aug 11, 2011 07:28:57 PM) Why you taken Tan and why you not taken cos ?

 Bhupal said: (Tue, Sep 6, 2011 01:21:36 PM) 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: (Tue, Sep 6, 2011 01:21:36 PM) 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: (Tue, Sep 6, 2011 01:21:36 PM) 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: (Fri, Oct 21, 2011 02:39:09 PM) tan is because sin/cos.

 Sanjana said: (Fri, Nov 25, 2011 01:50:40 PM) We can find square roots of any numbers by a special type of division or a method known as column method.

 Anish Kumar said: (Wed, Jan 11, 2012 10:09:34 PM) We can also able to find the answer using sin and cos. But more step is needed.

 Sahil said: (Thu, Feb 9, 2012 08:24:08 PM) How to calculate (root 3 + 1) manually, is there any way ?

 Shro said: (Mon, Feb 20, 2012 01:15:44 PM) @Sahil square root of 3 is 1.73. So ,add 1.73 + 1 = 2.73

 Ram said: (Mon, Mar 11, 2013 02:57:11 PM) How can you write AD=AB?