Question

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` , c = 3

Answer 1

`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`

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]