How do I draw the right triangle ABC whose sides have the following values given below, and then find the six trigonometric functions of each triangle’s angle A? a = 2, b= sqrt5√5 , c = 3

1 Answer
Binayaka C.
Jul 23, 2018

sin theta = b/c=sqrt5/3, cos theta = a/c=2/3 , tan theta= b/a=sqrt 5/2 , csc theta = c/b=3/sqrt 5 , sec theta= c/a=3/2 ,cot theta= a/b=2/sqrt 5sinθ=bc=√53,cosθ=ac=23,tanθ=ba=√52,cscθ=cb=3√5,secθ=ca=32,cotθ=ab=2√5

Explanation:

a= 2 :. a^2=4 , b=sqrt 5 :. b^2=5 , c=3 :. c^2=9

a^2+b^2= 5+4=9=c^2:. a^2+b^2= c^2 ; a,b,c are

adjacent side , opposite side and hypotenuse of the right

triangle. To be drawn making sides a and b at right angle

and c as hypotenuse of the triangle.

Let theta be the angle between adjacent side a

and hypotenuse c , then , sin theta = b/c=sqrt5/3

cos theta = a/c=2/3 , tan theta= b/a=sqrt 5/2 ,

csc theta = c/b=3/sqrt 5 , sec theta= c/a=3/2 ,

cot theta= a/b=2/sqrt 5 [Ans]

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