Question

Let a vertical tower AB have its end A on the level ground. Let C be the midpoint of AB and P be a point on the ground such that
AP = 2AB . If angle BPC = Beta ,
Then tan beta is ........... ?



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Answer 1

Answer:

??

Step-by-step explanation:

Answer 2

Answer:

2/9

Step-by-step explanation:

Let AB=x. Then AP=2AB=2x

△ABP is a right-angled triangle with BP as hypotenuse.

By Pythagoras Theorem,

BP^2=AP^2+AB^2

BP^2=(2x)^2+x^2

BP^2=5x^2

⇒BP=√5x

AC=x/2

tanα= x/2/2x= 1/4

Now,

tan(α+β)= x/2x = 1/ 2

tanα+tanβ / 1−tanαtanβ = 1/2

⇒2(tanα+tanβ)=1−tanαtanβ

⇒2( 1/4+tanβ)=1− 1/4tanβ

⇒1/2+2tanβ=1− 1/4tanβ

⇒9/4tanβ=1/2

⇒tanβ= 2/9