A right triangle has two acute angles, θ 𝜃 and ϕ 𝜙 , so that cosϕ=x+0.2 cos ⁡ 𝜙 = 𝑥 + 0.2 and sinθ=2x−0.5 sin ⁡ 𝜃 = 2 𝑥 − 0.5 . What is the value of x?(1 point) Responses 1 1 0.7 0.7 0.07 0.07 10

Answer 1

In a right triangle, the angles \(\theta\) and \(\phi\) are related by the identity \(\theta + \phi = 90^\circ\). Therefore, we have the relationship:

\[ \cos \phi = \sin \theta \]

Given:

\[ \cos \phi = x + 0.2 \] \[ \sin \theta = 2x - 0.5 \]

Setting these equal based on the trigonometric identity:

\[ x + 0.2 = 2x - 0.5 \]

Now, let's solve for \(x\):

1. Rearranging the equation: \[ 0.2 + 0.5 = 2x - x \] \[ 0.7 = x \]

So, the value of \(x\) is:

\[ \boxed{0.7} \]