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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 8: Q.15 (page 553)

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say 鈥淣o triangle.鈥� $a = 1, b = 3, C = 40$

Short Answer

Expert verified

The remaining angles and sides of a triangle is $c = 2.32 A = 16 B = 124$

Step by step solution

01

Step 1. Given information

The given data is $a = 1, b = 3, C = 40$

02

Step 2. find the side c

Use cosines Rule $\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b}$

Here. $a = 1, b = 3, C = 40$

$\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} \cos 40 = \frac{1^{2} + 3^{2} - c^{2}}{2 * 1 * 3} \cos 40 = \frac{10 - c^{2}}{6} 10 - c^{2} = 4.6 c^{2} = 5.4 c = 2.32$

03

Step 3. Find the angle B

Use the Law of sines, $\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c}$

Here, $a = 1, b = 3, c = 2.32, C = 40$

$\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} . \frac{\sin A}{1} = \frac{S i n 40}{2.32} \sin A = 0.27 A = 16$

04

Step 4. Find the angle B

Since the angle A, B, and c are the angel of a triangle,

$A + B + C = 180 16 + B + 40 = 180 B = 180 - 56 B = 124$

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