Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 10 - Radical Expressions and Equations - 10-6 Trigonometric Ratios - Practice and Problem-Solving Exercises - Page 650: 42


The value for q=6.1 and the value for r=7.9.

Work Step by Step

This is a two-step problem as q and r must be found separately and then added together. Solving for q comes first because it allows us to solve for r using the same length of the base. Using the tan rule of opposite/base, the equation is modelled as $ tan17 = \frac{q}{20} $ . Multipling 20 to both sides will isolate q and give us an equation of $ tan17 * 20 = q $. Plugging in 0.305 for tan17 and simplfiying, we get a result of q=6.1. Solving for r uses the same idea of opposite/base. We add both angles of 17 and 18 to obtain the angle necessary for r, which is 35. The opposite length in this case is q+r. Since we already know q, the equation can be shown as $tan35 = (6.1 + r)/20 $. Multiplying both sides by 20 and simplifying for the left side will give us an equation of $ 14 = 6.1 + r $. Subtracting the 6.1 from the 14 then solves for r, which is 7.9.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.