NIMCET 2015 Question Paper with solutions

Question : 34 of 120

Marks: +1, -0

In a right angles triangle, the hypotenuse is four times the perpendicular drawn to it from the opposite vertex. The value of one of the acute angles is;

45°
30°
15°
none of these

Validate

Solution:

Let A8C is a right angle triangle and ∠B = 90°
We have AC = 4AD

Let BD = x
∴ AC = 4x
∠BDC = 90°
In ΔBDC,

\sinθ={BD}/{BC}

⇒BC=x/{\sinθ}

.......(i)
In ΔABC,

\cosθ={BC}/{AC}

⇒\cosθ={BC}/{4x}

⇒BC=4x\cosθ

....(ii)
From Eqs. (i) and (ii) we get

4x\cosθ=x/{\sinθ}

2\sinθ\cosθ=1/2

⇒\sin2θ=1/2

⇒2θ=30°⇒θ=15°

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