Question

A right triangle has two acute angles, θ and ϕ , so that cosϕ=x+0.2 and sinθ=2x−0.5 . What is the value of x?(1 point) Responses

Answer 1

To find the value of x, we need to solve the given equations for x.

From the first equation, cosϕ = x + 0.2, we can solve for x by subtracting 0.2 from both sides:
cosϕ - 0.2 = x

From the second equation, sinθ = 2x - 0.5, we can solve for x by adding 0.5 to both sides and then dividing by 2:
sinθ + 0.5 = 2x
(1/2)(sinθ + 0.5) = x

Since both x values are equal, we can set them equal to each other and solve for x:
cosϕ - 0.2 = (1/2)(sinθ + 0.5)

Now we can substitute the given values of cosϕ and sinθ into the equation to find x.