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Q.

Find the smallest angle, if one acute angle of the right-angled triangle is half of the other.


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a

90o

b

60o

c

40o

d

30o  

answer is D.

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Detailed Solution

Given that, the acute angle is half of the other.
Let the acute angle be x. Then the other angle is 2x.
Drawing the figure from the given data.
Question ImageIn triangle ABC, the sum of angles of a triangle is 180o. So,
 ⟹ 90o+2x+x=180o  ⟹ 3x=180o-90o  ⟹ x=90o3  ⟹ x=30o
Hence, the angles are,
x=30o 2x=2×30o =60o.
Hence, 30o is the smallest angle.
Therefore, option 4 is correct.
 
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