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)

Question

Responses

1
1

0.7
0.7

10
10

0.07

Answer 1

To solve for \( x \) given the equations \( \cos \phi = x + 0.2 \) and \( \sin \theta = 2x - 0.5 \), we can use the property that in a right triangle, \( \theta + \phi = 90^\circ \). This means that:

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

Substituting our equations into this relationship gives us:

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

Now, we can solve for \( x \):

1. Move \( x \) from the right side to the left side: \[ 2x - x - 0.5 = 0.2 \]

2. Simplify the left side: \[ x - 0.5 = 0.2 \]

3. Add \( 0.5 \) to both sides: \[ x = 0.2 + 0.5 \]

4. Calculate the value: \[ x = 0.7 \]

Thus, the value of \( x \) is \( \boxed{0.7} \).