Question

Which trigonometric ratios are correct for triangle
ABC? Select three options.

Answer 1

Options (1), (3) and (4)

Explanation:

From ΔABC given in the picture,

By Pythagoras theorem

Hypotenuse² = (Leg 1)² + (Leg 2)²

BC² = AB² + AC²

(18)² = 9² + AC²

AC =

AC = cm

sin(C) =

=

=

sin(C) =

sin(B) =

=

=

cos(B) =

=

=

tan(B) =

=

=

=

tan(C) =

=

=

Therefore, Options (1), (3) and (4) are the correct options.Explanation:

Answer 2

Options (1), (3) and (4)

Explanation:

From ΔABC given in the picture,

By Pythagoras theorem

Hypotenuse² = (Leg 1)² + (Leg 2)²

BC² = AB² + AC²

(18)² = 9² + AC²

AC =
`√(324-81)`

AC =
`9√(3)` cm

sin(C) =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

=
`(AB)/(BC)`

=
`(9√(3))/(18)`

sin(C) =
`(√(3) )/(2)`

sin(B) =
`(AC)/(BC)`

=
`(9)/(18)`

=
`(1)/(2)`

cos(B) =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

=
`(9√(3))/(18)`

=
`(√(3) )/(2)`

tan(B) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

=
`(AC)/(AB)`

=
`(9)/(9√(3) )`

=
`(1)/(√(3) )`

tan(C) =
`(AB)/(AC)`

=
`(9√(3))/(9)`

=
`√(3)`

Therefore, Options (1), (3) and (4) are the correct options.