/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 17 Use the Law of Cosines to solve ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 17

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. $$A=120^{\circ}, \quad b=6, \quad c=7$$

Short Answer

Expert verified
The length of side a is approximately 9.13. The measures of angles B and C are approximately 46.18 and 13.82 degrees, respectively.

Step by step solution

01

Application of Law of Cosines to find side a

The Law of Cosines states that \(a^2 = b^2 + c^2 - 2bc \cos A\). Substitute the given values into this equation to solve for 'a'. This gives \(a^2 = 6^2 + 7^2 - 2(6)(7) \cos 120^\circ = 83.40\). Take the square root of each side to solve for 'a', which will be \(a \approx 9.13\).
02

Application of Law of Cosines to find angle B

We rearrange the law of cosines to solve for the angle B, as follows: \(\cos B = \frac{b^2 + c^2 - a^2}{2bc}\). Substituting the given/solved values into this equation to find 'B'. This gives \(\cos B = \frac{6^2 + 7^2 - (9.13)^2}{2(6)(7)}\). Thus, \(B \approx 46.18^\circ\).
03

Use angles sum up to 180 degrees to find angle C

In a triangle, the sum of all internal angles adds up to 180 degrees. Therefore, we have \[B + C + 120 = 180\] Solving for 'C' will give us \(C \approx 180 - B - 120 = 13.82^\circ\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine whether the statement is true or false. Justify your answer. $$\sin \left(x-\frac{\pi}{2}\right)=-\cos x$$

Use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine. $$\sin ^{2} 2 x \cos ^{2} 2 x$$

Use the formulas given in Exercises 89 and 90 to write the trigonometric expression in the following forms.$$\text { (a) } \sqrt{a^{2}+b^{2}} \sin (B \theta+C)$$ $$\text { (b) } \sqrt{a^{2}+b^{2}} \cos (B \theta-C)$$ $$3 \sin 2 \theta+4 \cos 2 \theta$$

Find all solutions of the equation in the interval \([0,2 \pi)\). $$\cos (x+\pi)-\cos x-1=0$$

Use the sum-to-product formulas to rewrite the sum or difference as a product. $$\sin 3 \theta+\sin \theta$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.