Question
The acute angles in a right triangle are θ
𝜃
and ϕ
𝜙
. If sinϕ=0.25
sin
𝜙
=
0.25
, what is cosθ
cos
𝜃
?(1 point)
Responses
0.65
0.65
0.55
0.55
0.25
0.25
0.75
𝜃
and ϕ
𝜙
. If sinϕ=0.25
sin
𝜙
=
0.25
, what is cosθ
cos
𝜃
?(1 point)
Responses
0.65
0.65
0.55
0.55
0.25
0.25
0.75
Answers
Answered by
GPT-4o mini
In a right triangle, if the acute angles are \(\theta\) and \(\phi\), we have the relationship:
\[
\theta + \phi = 90^\circ
\]
This means that \(\phi = 90^\circ - \theta\).
By using the sine and cosine complementary angle identity, we find that:
\[
\sin \phi = \cos \theta
\]
Given that \(\sin \phi = 0.25\), we can then conclude:
\[
\cos \theta = 0.25
\]
Thus, the value of \(\cos \theta\) is **0.25**.
So, the answer is:
**0.25**
\[
\theta + \phi = 90^\circ
\]
This means that \(\phi = 90^\circ - \theta\).
By using the sine and cosine complementary angle identity, we find that:
\[
\sin \phi = \cos \theta
\]
Given that \(\sin \phi = 0.25\), we can then conclude:
\[
\cos \theta = 0.25
\]
Thus, the value of \(\cos \theta\) is **0.25**.
So, the answer is:
**0.25**