/*! 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 55 Describe a strategy for solving ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 55

Describe a strategy for solving an SAS triangle.

Short Answer

Expert verified
A strategy to solve an SAS triangle involves the following steps: (1) Understand what is given and what is required; (2) Use the law of cosines to find the unknown side; (3) Use the law of sines to find one unknown angle; (4) Subtract the two known angles from 180 to find the remaining angle.

Step by step solution

01

Understanding the Problem

Given a triangle where two of its sides and the included angle are known. This is denoted as an SAS triangle. The task is to find the other dimensions of the triangle. The dimensions are the remaining side and two angles.
02

Use the Law of Cosines

To find the unknown side of the SAS triangle, use the law of cosines. This is given by \(c^2 = a^2 + b^2 - 2ab\cos(C)\), where 'a' and 'b' are the known sides, 'C' is the known included angle, and 'c' is the side to be found. Substitute the known values into the equation and solve for 'c'.
03

Use the Law of Sines to Find One of the Unknown Angles

After finding the unknown side, use the law of sines to find one of the unknown angles. The law of sines states that the ratio of a side length to the sine of its opposite angle is constant. Use one of the already determined sides and its opposite angles. This will give an equation that can be solved for the unknown angle by taking the inverse sine.
04

Find the Remaining Angle

Since the sum of the angles in a triangle is 180 degrees, subtract the two known angles from 180 to find the remaining angle.

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

Use a graphing utility to graph each butterfly curve. Experiment with the range setting, particularly \(\theta\) step, to produce a butterfly of the best possible quality. $$r=\cos ^{2} 5 \theta+\sin 3 \theta+0.3$$

Find \(\text {pro}_{\mathbf{w}} \mathbf{V}\) Then decompose v into two vectors, \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2},\) where \(\mathbf{v}_{1}\) is parallel to \(\mathbf{w}\) and \(\mathbf{v}_{2}\) is orthogonal to \(\mathbf{w}.\) $$\mathbf{v}=3 \mathbf{i}-2 \mathbf{j}, \quad \mathbf{w}=2 \mathbf{i}+\mathbf{j}$$

Exercises \(81-83\) will help you prepare for the material covered in the next section. Find the obtuse angle \(B,\) rounded to the nearest degree, satisfying $$ \cos B=\frac{6^{2}+4^{2}-9^{2}}{2 \cdot 6 \cdot 4} $$

What are parallel vectors?

Use a graphing utility to graph \(r=1+2 \sin n \theta\) for \(n=1,2,3,4,5,\) and \(6 .\) Use a separate viewing screen for each of the six graphs. What is the pattern for the number of large and small petals that occur corresponding to each value of \(n\) ? How are the large and small petals related when \(n\) is odd and when \(n\) is even?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.