Question

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

0.25
0.25

0.55
0.55

0.65
0.65

0.75

Answer 1

In a right triangle, the acute angles \( \theta \) and \( \phi \) are complementary, which means that:

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

From the definition of sine and cosine for complementary angles, we have:

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

Given that \( \sin \phi = 0.25 \), we can directly find \( \cos \theta \):

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

Therefore, the value of \( \cos \theta \) is \( 0.25 \).

So the correct response is:

0.25