IDNLearn.com: Where your questions meet expert advice and community insights. Our Q&A platform is designed to provide quick and accurate answers to any questions you may have.
What is the greatest number of acute angles that a right triangle can contain?
To solve the question of determining the greatest number of acute angles in a right triangle, let's start by understanding the properties of right triangles and angles.
1. Properties of a Right Triangle: - A right triangle contains one angle that is exactly [tex]\(90^\circ\)[/tex]. - A triangle has three angles that sum up to [tex]\(180^\circ\)[/tex].
2. Understanding Acute Angles: - An acute angle is any angle that is less than [tex]\(90^\circ\)[/tex].
Given that one angle in a right triangle is always [tex]\(90^\circ\)[/tex], we focus on the other two angles.
3. Calculating the Other Two Angles: - Let [tex]\(A\)[/tex] and [tex]\(B\)[/tex] be the measures of the other two angles in the right triangle. - Since the sum of the angles in any triangle is [tex]\(180^\circ\)[/tex], we have the equation: [tex]\[
A + B + 90^\circ = 180^\circ
\][/tex] - Simplifying the above equation: [tex]\[
A + B = 90^\circ
\][/tex]
4. Determining the Nature of [tex]\(A\)[/tex] and [tex]\(B\)[/tex]: - Both [tex]\(A\)[/tex] and [tex]\(B\)[/tex] must be less than [tex]\(90^\circ\)[/tex] to satisfy the equation [tex]\(A + B = 90^\circ\)[/tex]. - Hence, both [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are acute angles (they are less than [tex]\(90^\circ\)[/tex]).
5. Greatest Number of Acute Angles: - Since both [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are acute and there are no other angles in the right triangle apart from the [tex]\(90^\circ\)[/tex] angle, the greatest number of acute angles in a right triangle is [tex]\(\boxed{2}\)[/tex].
Thus, the correct answer to the question is [tex]\( \text{A. 2} \)[/tex].
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.
