   # Solve each triangle using the labels as shown in Illustration 1 (round lengths of sides to three significant digits and angles to the east tenth of a degree): ILLUSTRATION 1 a = 38 , 500 mi , b = 67 , 500 mi , c = 47 , 200 mi ### Elementary Technical Mathematics

12th Edition
Dale Ewen
Publisher: Cengage Learning
ISBN: 9781337630580

#### Solutions

Chapter
Section ### Elementary Technical Mathematics

12th Edition
Dale Ewen
Publisher: Cengage Learning
ISBN: 9781337630580
Chapter 14.5, Problem 5E
Textbook Problem
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## Solve each triangle using the labels as shown in Illustration 1 (round lengths of sides to three significant digits and angles to the east tenth of a degree): ILLUSTRATION 1 a = 38 , 500  mi , b = 67 , 500  mi ,   c = 47 , 200  mi

To determine

To calculate: The round lengths of sides to three significant digits and angles to the nearest tenth

Of a degree for the provided triangle if a=38500mi,b=67500mi and c=47200mi. ### Explanation of Solution

Given Information:

The provided triangle is shown below:

Where a, b and c are sides. A, B and C are the values of angle.

Here,

a=38500mi,b=67500mi and c=47200mi

Formula used:

Law of cosines:

a2=b2+c22bccosA

Law of sine:

asinA=bsinB=csinC

Where a, b and c are sides. A, B and C are the values of angle.

Multiplication property of equality:

A=B and AC=BC Are equivalent where C0.

Calculation:

Consider the provided triangle diagram with provided value,

a=38500mi,b=67500mi and c=47200mi

Use law of cosines a2=b2+c22bccosA to find angle A.

Now substitute the value a=38500mi,b=67500mi and c=47200mi in a2=b2+c22bccosA

Therefore,

(38500)2=(67500)2+(47200)22(67500)(47200)cosA1482250000=4556250000+22278400006372000000cosA14822500006784090000=6372000000cosA5301840000=6372000000cosA

Further simplify,

cosA=53018400006372000000cosA=0

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