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 - Chapter Test - Page 537: 15


$x = 18.7$

Work Step by Step

Since we have the measure of one angle and the measure of the side opposite to that angle, we can use the sine ratio to find $x$, which is the hypotenuse of the triangle. The sine ratio is given as follows: sin $A = \frac{opposite}{hypotenuse}$ Let's plug in what we know: sin $40^{\circ} = \frac{12}{x}$ Multiply each side by $x$: sin $40^{\circ}(x) = 12$ Divide both sides by sin $40^{\circ}$ to solve for $x$: $x = 18.7$
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