Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 1 - Review Exercises - Page 41: 18

Answer

$m=45$ and $n=60$

Work Step by Step

Similar triangles have corresponding sides in proportion. Side of length 75 corresponds to side of length 50 and side of length n corresponds to side of length 40. This leads to the following proportion: $\frac{75}{50}=\frac{n}{40}$ Solving, $75\times40=50\times n$ $3000=50n$ Dividing both sides by $50, $$n=60$. Side of length 75 corresponds to side of length 50 and side of length m corresponds to side of length 30. This leads to the following proportion: $\frac{75}{50}=\frac{m}{30}$ Solving, $75\times30=50\times m$ $2250=50m$ Dividing both sides by $50, $$m=45$.
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