Question
The acute angles in a right triangle are \( \theta \) and \( \phi \). if \( \sin \phi=0.25 \), what is \( \cos \theta \) ? (t point) 0.25 0.55 0.75 0.65 Check answer Remaining Attempts : 3
Ask by Greene Joseph. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \cos \theta = 0.25 \)
Solution
In a right triangle, the two acute angles \( \theta \) and \( \phi \) satisfy the relationship:
\[
\theta + \phi = 90^\circ
\]
This implies:
\[
\cos \theta = \sin (90^\circ - \theta) = \sin \phi
\]
Given that \( \sin \phi = 0.25 \), it directly follows that:
\[
\cos \theta = 0.25
\]
**Answer:** 0.25
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Beyond the Answer
In a right triangle, the sum of the acute angles \( \theta \) and \( \phi \) is \( 90^\circ \). Therefore, \( \cos \theta = \sin \phi \). Given that \( \sin \phi = 0.25 \), it follows that \( \cos \theta = 0.25 \). To double-check the calculations, we can find \( \phi \)’s angle using \( \sin(\phi) = 0.25 \). This further implies that \( \theta = 90^\circ - \phi \), ensuring that you employ the complementary angle relationship in your future angle endeavors!
