/*! 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 15 Use the Law of Cosines to solve ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 15

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. $$B=10^{\circ} 35^{\prime}, \quad a=40, \quad c=30$$

Short Answer

Expert verified
Once we've carried out the above steps, we should have the lengths of all three sides of the triangle, and the measures of all three angles in decimal degrees.

Step by step solution

01

Convert Minutes to Decimal Degrees

First convert the angle B from degrees and minutes to decimal degrees. The given angle B is \(10^{\circ} 35^{\prime}\). In 1 degree there are 60 minutes, so to convert we do: \(10 + \frac{35}{60} = 10.58\) degrees.
02

Compute Side b

The next step is to calculate the unknown side b using the Law of Cosines. The Law of Cosines states \(b^2 = a^2 + c^2 - 2ac \cos B\). Plugging in the known values we'll get: \(b^2 = 40^2 + 30^2 - 2 \times 40 \times 30 \times \cos (10.58)\). Solving this we'll get the length of side b.
03

Compute Angles A and C

Now we can compute the angles A and C using the Law of Sines. It states that the ratio of a side's length to the sine of its opposite angle is constant for all three sides. This allows us to write the following equations: \(\frac{a}{\sin A} = \frac{b}{\sin B}\) to get the angle A and \(\frac{c}{\sin C} = \frac{a}{\sin A}\) to get the angle C. Solving these we'll get the angles A and 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

Solve the multiple-angle equation. $$\cos \frac{x}{2}=\frac{\sqrt{2}}{2}$$

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

Write the expression as the sine, cosine, or tangent of an angle. $$w\sin 3 \cos 1.2-\cos 3 \sin 1.2$$

Solve the multiple-angle equation. $$\cos 2 x=\frac{1}{2}$$

Find the exact value of each expression. (a) \(\cos \left(120^{\circ}+45^{\circ}\right)\) (b) \(\cos 120^{\circ}+\cos 45^{\circ}\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

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.