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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. 11 (page 535)

Solve the triangle

Short Answer

Expert verified

The solution is

$c = 3.75, A = 29.54 掳, B = 55.46 掳$

Step by step solution

01

Step1. Given information

The figure is

02

Step2. Formula used

$c^{2} = a^{2} + b^{2} - 2 a b . \cos C, \cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c},$

03

Step3. Calculation

$W e h a v e, a = 2, b = 3, C = 95 掳 W e k n o w c^{2} = a^{2} + b^{2} - 2 a b . \cos C = 2^{2} + 3^{2} - 2.2.3 . \cos 95 掳 = 4 + 9 - 12 (- . 087) = 13 + 1.044 = 14.044 c = \sqrt{14.044} = 3.75 A g a i n, \cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{3^{2} + {(3.75)}^{2} - 2^{2}}{2.3 . (3.75)} = \frac{9 + 14.0625 - 4}{22.5} = \frac{19.0625}{22.5} = 0.87 A = \cos^{- 1} (0.87) = 29.54 掳 A g a i n w e k n o w A + B + C = 180 掳 29.54 掳 + B + 95 = 180 掳 B = 180 掳 - 124.54 掳 = 55.46 掳$

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Most popular questions from this chapter

Given two sides and the included angle, the first thing to do to solve the triangle is to use the Law of Sines .

Find an exact value of each expression, without using a calculator $\cos^{2} 40 + \cos^{2} 50$

The motion of an object obeys the equation $d = 4 \cos (6 t)$ Such motion is described as ______ ______ . The number 4

is called the _____.

In the given problem solve the triangle using either the law of sines or law of cosines-

$B = 35 掳, C = 65 掳, a = 15$

In the given problem solve the triangle using either the law of sines or law of cosines-

$A = 10 掳, a = 3, b = 10$

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