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# Which statement can you conclude from the information given? Given: (In  right...

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Which statement can you conclude from the information given?

Given: (In  right triangle) sinA=a/c,   sin B = b/c,  m<A + m<B = 90 degrees,

cos A= b/c,  cos B = a/c,   a^2+b^2=c^2,  tan A = a/b,   tan B b/a

(A) sin A = cos B

(B) cos A = sin (90-A)

(C) sin^2 B + cos^2 B = 1

(D) All of these

Posted by novjb on September 4, 2013 at 12:30 AM via web and tagged with geometry, math, trigometry

College Teacher

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Given: In a right triangle ABC (refer to the attached image) `sinA=a/c` ,   `sin B = b/c` ,  `mltA + mltB = 90` degrees,

`cos A= b/c` ,  `cos B = a/c` ,   `a^2+b^2=c^2` ,  `tan A=a/b` ,   `tan B=b/a`

(A) `sin A=(BC)/(BA)=a/c` and `cos B=(BC)/(BA)=a/c`

Hence, `sin A = cos B.`

(B) `cos A =b/c `

`sinB=b/c`

`rArr sin(90-A)=b/c` ............(since `mltA + mltB = 90` degrees )

Hence, `cos A = sin (90-A)`

(C) `sin^2 B + cos^2 B `

`=(b/c)^2+(a/c)^2`

`=(b^2+a^2)/c^2`

`=c^2/c^2` ....................(since `a^2+b^2=c^2` )

`=1`

Therefore, option D) All of these, is the best conclusion.

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Posted by llltkl on September 4, 2013 at 1:32 AM (Answer #1)