Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.6 Right Triangle Trigonometry - Concept and Vocabulary Check - Page 665: 7

Answer

The given statement is false. The correct statement is “The side of a right triangle opposite an acute angle does not form the acute angle’s sides.”

Work Step by Step

To better understand, first draw a right angle triangle \[\vartriangle ABC\] and observe all the three angles. On observing one may find that there are two acute angles, that is, \[\measuredangle A\]and \[\measuredangle C\] excluding the angle at which the triangle is being right angled, that is, \[\measuredangle B\]. Further, one can also find and conclude that the side opposite to \[\measuredangle C\] is a right angle, right angled at \[B\]. This angle is not an acute angle. Hence, the given statement is \[\text{false}\]. The correct statement is “The side of a right triangle opposite an acute angle does not form the acute angle’s sides.”
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