/*! 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 24 Use the Law of Cosines to solve ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 24

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. $$C=101^{\circ}, \quad a=\frac{3}{8}, \quad b=\frac{3}{4}$$

Short Answer

Expert verified
The measurements of the triangle are side c rounded to two decimal places, and angles A and B also approximated to two decimal places.

Step by step solution

01

Find the length of side c

Use the Law of Cosines. The formula is \(c = \sqrt{a^{2} + b^{2} - 2ab\cos{C}}\). Substituting the given values gives \(c = \sqrt{(\frac{3}{8})^{2} + (\frac{3}{4})^{2} - 2*\frac{3}{8}*\frac{3}{4}\cos{101}}\). Round the result to two decimal places.
02

Find Angle A

Use the Law of Cosines to calculate angle A. Re-arranging the Law of Cosines gives \(A = \arccos{\frac{b^{2} + c^{2} - a^{2}}{2bc}}\). Substitute the values obtained for b, c and a (with a known value), then calculate angle A by applying the inverse cosine function. Remember to convert the angle from radians to degrees.
03

Find Angle B

Knowing that in a triangle, the sum of the angles equals 180 degrees, subtract the two known angles (A and C) from 180 to find angle B. That is, \(B = 180 - A - C\).

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

Simplify the expression algebraically and use a graphing utility to confirm your answer graphically. $$\cos (\pi+x)$$

Use the product-to-sum formulas to rewrite the product as a sum or difference. $$7 \cos (-5 \beta) \sin 3 \beta$$

Use the formulas given in Exercises 89 and 90 to write the trigonometric expression in the following forms.$$\text { (a) } \sqrt{a^{2}+b^{2}} \sin (B \theta+C)$$ $$\text { (b) } \sqrt{a^{2}+b^{2}} \cos (B \theta-C)$$ $$3 \sin 2 \theta+4 \cos 2 \theta$$

Verify the identity. $$\cos (n \pi+\theta)=(-1)^{n} \cos \theta, \quad n$ is an integer$$

Find the exact value of the trigonometric expression given that \(\sin u=-\frac{7}{25}\) and \(\cos v=-\frac{4}{5} .\) (Both \(u\) and \(v\) are in Quadrant III.) $$\sec (v-u)$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Applied 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.