Consider the following.

Question

Find the length of the third side of the triangle in terms of x.

= ________

Find 𝜃 in terms of x for all three inverse trigonometric functions.

 𝜃 = sin^-1(_____)

𝜃 = cos^-1(_____)

𝜃 = tan^-1(_____)

Answer 1

Let the unknown side be r

r sinθ = (x + 2)

r = (x + 2)/sinθ = The length of the third side

r cosθ = 3 ⇒ cosθ = 3/r so θ = cos^-1(3/r)

r sinθ = x + 2 ⇒ sinθ = (x + 2)/r soθ = sin^-1(x + 2)/r

tanθ = (x + 2)/3 so θ = tan^-1(x + 2)/3