/*! 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 14 Use the Law of Cosines to solve ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 14

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. $$A=48^{\circ}, \quad b=3, \quad c=14$$

Short Answer

Expert verified
After performing all of these steps, rounding to two decimal places, 'a' should be found to be about 13.37 units, angle 'B' is approximately 9.93 degrees, and angle 'C' is approximately 122.07 degrees.

Step by step solution

01

Apply Law of Cosines to find 'a'

The Law of Cosines can be written as \(a^{2} = b^{2} + c^{2} - 2bc \cos(A)\). Substituting the known values, we get \(a^{2} = 3^{2} + 14^{2} - 2 \cdot 3 \cdot 14 \cdot \cos(48^{\circ})\). Solve the equation to find the value of 'a'.
02

Calculate angle B using the Law of Sines or Law of Cosines

To find angle B, use the Law of Sines, as it requires fewer computations: \( \frac{b}{\sin(B)} = \frac{a}{\sin(A)} \). This can be rewritten as: \( \sin(B) = \frac{b \cdot \sin(A)}{a} \). Substituting the given values and then taking the inverse sine, we get angle B.
03

Calculate angle C

Now that we have two of the angles in the triangle, we can calculate the third angle using the property that the sum of angles in a triangle equals 180 degrees. So, \(C = 180^{\circ} - A - B\). Substitute A and B with their calculated values to find C.

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

Find the exact values of the sine, cosine, and tangent of the angle. $$\frac{7 \pi}{12}=\frac{\pi}{3}+\frac{\pi}{4}$$

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$6 \sin ^{2} x-7 \sin x+2=0$$

Use the Quadratic Formula to solve the equation in the interval \([0,2 \pi)\). Then use a graphing utility to approximate the angle \(x\). $$4 \cos ^{2} x-4 \cos x-1=0$$

Find the exact value of the expression. $$\sin \frac{\pi}{12} \cos \frac{\pi}{4}+\cos \frac{\pi}{12} \sin \frac{\pi}{4}$$

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$4 \sin ^{3} x+2 \sin ^{2} x-2 \sin x-1=0$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Statistics

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.