/*! 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 19 Use the Law of Cosines to solve ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 19

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
The triangle can be solved using the Law of Cosines. This results in the finding of side b and angles A and C after the necessary calculations. All values are rounded to two decimal places.

Step by step solution

01

Convert Angle B to Decimal Degrees

To convert the angle B from degrees, minutes to decimal degrees, use the formula: Degrees + (Minutes/60).Therefore, \( B=10+35/60=10.583^{\circ} \)
02

Apply the Law of Cosines

Once angle B has been converted, use the Law of Cosines to find the length of side b. The formula is: \( b^{2}=a^{2}+c^{2}-2ac*cos(B) \).Substitute given values: \( b^{2}=40^{2}+30^{2}-2*40*30*cos(10.583) \).Calculate the value of b using a calculator.
03

Solve for Angle A using Law of Cosines

Now find angle A using the derived value of side b and the Law of Cosines in terms of angle A. The formula is: \( A=cos^{-1}[(b^{2}+c^{2}-a^{2})/(2bc)] \).Substitute known values into formula and solve for Angle A. Be sure to convert the result to degrees.
04

Calculate Angle C

Finally, calculate the third angle C by using the fact that the sum of angles in a triangle is always 180 degrees. Therefore, \( C = 180- A - B \).

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 value of the expression. $$\cos 120^{\circ} \cos 30^{\circ}+\sin 120^{\circ} \sin 30^{\circ}$$

Use the sum-to-product formulas to rewrite the sum or difference as a product. $$\cos \left(\theta+\frac{\pi}{2}\right)-\cos \left(\theta-\frac{\pi}{2}\right)$$

Find the exact value of the expression. $$\frac{\tan (5 \pi / 6)-\tan (\pi / 6)}{1+\tan (5 \pi / 6) \tan (\pi / 6)}$$

Prove the identity. $$\sin \left(\frac{\pi}{6}+x\right)=\frac{1}{2}(\cos x+\sqrt{3} \sin x)$$

Use a graphing utility to approximate the solutions of the equation in the interval \([0,2 \pi)\). $$\cos \left(x-\frac{\pi}{2}\right)-\sin ^{2} x=0$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

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.