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Q.

If tanθ=0.75  , then sin θ = ____.


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Detailed Solution

If tanθ=0.75  , then sin θ = 3 5  .
Given that, tanθ=0.75  .
Tangent is a ratio of the side opposite to the angle θ   by side adjacent to the angle θ  . If k is any positive integer,
tanθ= 75k 100k ⇒ Opposite side Adjacent side = 3k 4k  
Form a triangle with respect to θ   with opposite side as BC and adjacent side (AB).
Question ImageBy applying Pythagoras theorem, we get,
A C 2 =B C 2 +A B 2 ⇒A C 2 =9 k 2 +16 k 2 ⇒A C 2 =25 k 2 ⇒AC=5k  
sinθ= Opposite side Hypotenuse ⇒sinθ= BC AC ⇒sinθ= 3k 5k ⇒sinθ= 3 5  
So, the value of sinθ   is 3 5  .
Hence, the correct answer is 3 5  .
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