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)

10
0.07
1
0.7

Answer 1

plz pick one of my choices

Answer 2

The values of cosine and sine have a range of -1 to 1. The given information states that cosϕ = x + 0.2, so the possible range of values for cosϕ is between -0.8 and 1.2.

From the given information, sinθ = 2x - 0.5. Since sinθ has a range of -1 to 1, we can set up an equation to find the possible values of x:

-1 ≤ 2x - 0.5 ≤ 1

Adding 0.5 to all parts of the inequality, we have:

-0.5 ≤ 2x ≤ 1.5

Dividing all parts of the inequality by 2, we get:

-0.25 ≤ x ≤ 0.75

Therefore, the value of x must be between -0.25 and 0.75. None of the given answer choices fall within this range.

Answer 3

From the given equation sinθ = 2x - 0.5, we can solve for x by rearranging the equation:

2x = sinθ + 0.5

x = (sinθ + 0.5)/2

Now, let's substitute the given value sinθ = 2x - 0.5 into the equation:

x = (2x - 0.5 + 0.5)/2
x = 2x/2
x = x

This implies that x can have any value and is not determined by the given information. Therefore, none of the given answer choices can be determined as the value of x.