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Question

If the sides of an right triangle are in AP, then the sum of the sines of the two acute angles is

A
75
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B
43
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C
5125+12
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D
None of the above
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Solution

The correct option is A 75
Given sides are in A.P
So let sides be ad,a,a+d
Since a+d is largest so it will become hypotenuse.
Using pythagoras
(ad)2+a2=(a+d)2
On solving the above equation we get
a2=4ad
Since a can be equal to 0
So we get a=4d
Now after puttinga=2d our sides of triangles are
3d,4d,5d
sine of acute angles are3d5d and 4d5d =35 and 45
So their sum will be 4+35 =75
Hence, the answer is 75.

851679_861935_ans_e53c8d9f8b8241c1b4f71ad62e9dbe34.png

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