/*! 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 21 Use the Law of Sines to solve th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 21

Use the Law of Sines to solve the triangle. Round your answers to two decimal places. $$A=145^{\circ}, \quad a=14, \quad b=4$$

Short Answer

Expert verified
Angle B is approximately \(9.45\) degrees, angle C is approximately \(25.55\) degrees and side c is approximately \(5.91\) units long.

Step by step solution

01

Find angle B

Use the law of sines to solve for B. Re-arrange the formula to solve for B: \(B = \sin^-1(\frac{b \sin A}{a}) = \sin^-1(\frac{4 \sin 145}{14})\). Using the table for sin values or a calculator, we find \(B \approx 9.45\) degrees. Remember to round to two decimal places.
02

Calculate angle C

Since the sum of angles in a triangle is 180 degrees, we calculate angle C as follows: \(C = 180 - A - B = 180 - 145 - 9.45 = 25.55\) degrees.
03

Find side c

We can now use the law of sines again to find side c using the formula \(\frac{c}{\sin C} = \frac{a}{\sin A}\), it rearranges to \(c = a \sin C/ \sin A = 14 * \sin 25.55 / \sin 145 \approx 5.91\).

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 all solutions of the equation in the interval \([0,2 \pi) .\) Use a graphing utility to graph the equation and verify the solutions. $$\sin \frac{x}{2}+\cos x-1=0$$

Use the half-angle formulas to simplify the expression. $$\sqrt{\frac{1+\cos 4 x}{2}}$$

Verify the identity. $$(\sin x+\cos x)^{2}=1+\sin 2 x$$

Prove the identity. $$\sin \left(\frac{\pi}{2}-x\right)=\cos x$$

Find all solutions of the equation in the interval \([0,2 \pi) .\) Use a graphing utility to graph the equation and verify the solutions. $$\frac{\cos 2 x}{\sin 3 x-\sin x}-1=0$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

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.