Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 8 - Right Triangles and Trigonometry - 8-3 Trigonometry - Practice and Problem-Solving Exercises - Page 512: 49


Let's rewrite the expression on the left in terms of the ratios of sides: sin $B$ = $\frac{opposite}{hypotenuse}$ cos $B$ = $\frac{adjacent}{hypotenuse}$ Let's plug in what we know into the equation we are given: $\frac{b^2}{c^2} + \frac{a^2}{c^2} = 1$ Rewrite the equation so that the fraction is combined into one: $\frac{a^2 + b^2}{c^2} = 1$ We now look at the Pythagorean theorem, which relates the sides to the hypotenuse. The Pythagorean theorem is given by the following formula: $a^2 + b^2 = c^2$ We can replace $a^2 + b^2$ with $c^2$: $\frac{c^2}{c^2} = 1$ Simplify the fraction by dividing both the numerator and denominator by their greatest common factor: $1 = 1$ The identity is verified as being true.

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