Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.4 Solving Right Triangles - 2.4 Exercises: 34

Answer

$a = 306~m$ $b = 1248~m$ $B = 76^{\circ}12'$

Work Step by Step

We can convert angle A to degrees: $A = 13^{\circ}47' = (13+\frac{47}{60})^{\circ} = 13.8^{\circ}$ We can use angle A and angle C to find angle B: $B = 180^{\circ}-90^{\circ}-13.8^{\circ} = 76.2^{\circ}$ $B = 76.2^{\circ}$ which is $76^{\circ}12'$ We can use angle A and $c$ to find $b$: $cos~A = \frac{b}{c}$ $b = (c)~cos~A$ $b = (1285~m)~cos(13.8^{\circ})$ $b = 1248~m$ We can use the Pythagorean theorem to find a: $a^2 = c^2-b^2$ $a = \sqrt{c^2-b^2}$ $a = \sqrt{(1285~m)^2-(1248~m)^2}$ $a = 306~m$
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