The acute angles in a right triangle are θ and ϕ . If sinϕ=0.25 , what is cosθ ?(1 point)Responses0.250.250.650.650.750.750.55

Answer 1

In a right triangle, the sum of the acute angles \( \theta \) and \( \phi \) is \( 90^\circ \). Therefore, we have:

\[ \theta + \phi = 90^\circ \]

This means that:

\[ \theta = 90^\circ - \phi \]

Using the co-function identity for cosine and sine, we know that:

\[ \cos(\theta) = \sin(90^\circ - \theta) = \sin(\phi) \]

Given that \( \sin(\phi) = 0.25 \), we can substitute:

\[ \cos(\theta) = \sin(\phi) = 0.25 \]

Thus, the value of \( \cos \theta \) is:

\[ \boxed{0.25} \]