Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 11 - Section 11.4 - Applications with Acute Triangles - Exercises - Page 527: 15

Answer

15.21425 sq.ft

Work Step by Step

1. Draw the two diagonals; diagonal QN is further referred to as "x" and PM as "y". 2. As the diagonals are split in two, label each half as half x (x/2) and half y (y/2). 3. You can now find the measure of x and y by using basic trigonometric functions sine and cosine. 4a. $sin(12.5)=\frac{x/2}{6}$ 4b. $cos(12.5)=\frac{y/2}{6}$ 5a. $x=sin(12.5)*12$ 5b. $y=cos(12.5)*12$ 6a. $x=2.597275$ 6b. $y=11.715552$ 7. Now that we have the measures of both the diagonals, we can substitute them in the rhombus area formula to get our result. 8. $Area=\frac{1}{2}*d_{1}*d_{2}$. Here, d1 is x and d2 is y. 9. $Area=\frac{1}{2}*x*y$. Substituting the values in the equation we should get our result. 10. $Area=\frac{1}{2}*2.597275*11.715552$ 11. $Area=15.2142552$. Therefore $Area \approx 15.21425$
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