Double Triangle


Some Applications of Trigonometry - Concepts
Class - RRB Technician Grade I Signal Subjects
 
 
Concept Explanation
 

Double Triangle

DOUBLE TRIANGLE:

Let AB be a tower and B be its foot. On the horizontal line through B, take two points P and Q, Measure the length PQ.

Let PQ = a.

Let the angles of elevation of the top A of the tower as seen from P and Q be respectively large alpha and large beta large (beta >alpha ), then large angle APB=alpha ,angle AQB=beta

Let AB = x, BQ = y

From right angled large Delta ABP,tan alpha =frac{AB}{PB}=frac{x}{a+y}

large therefore a+y=xcot;alpha

From right angled large Delta ABQ,tan;beta =frac{AB}{BQ}=frac{x}{y}

large therefore ;y=x;cot;beta         ...............(ii)

From equations (i) and (ii)

large therefore ;a=x;cot;alpha -x;cot;beta

large Rightarrow ;x=frac{a}{cot;alpha -cot;beta }

Also, large y=x;cot;alpha -a

large Rightarrow ;y=frac{a;cot;alpha }{cot;alpha -cot;beta }-a;Rightarrow ;y=frac{a;cot;alpha -a(cot;alpha -cot;beta )}{cot;alpha -cot;beta };Rightarrow ;y=frac{a;cot;beta }{cot;alpha -cot;beta }

In the above case , P and Q are on the same side of the tower.

If the two points are on the opposit sides of the tower then from the adjoining figure, we get

large tan;alpha =frac{x}{PB}=x;cot;alpha ;;;and;;;tan;beta =frac{x}{BQ}or;BQ=x;cot;beta .

large therefore a=PB+BQ=x(cot;alpha +cot;beta )

large therefore x=frac{a}{cot;alpha +cot;beta }

and large y=BQ=x;cot;beta

Sample Questions
(More Questions for each concept available in Login)
Question : 1

A flagstaff of height h is mouted on the top of a building. From a point on the ground, the angles of elevation of the foot and top of the flagstaff are lambda and  beta respectively. If k is the height of the building, which of the following relationship is true?

Right Option : D
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Explanation
 
 


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