/*! 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 17 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 17

Use the Law of Sines to solve the triangle. Round your answers to two decimal places. $$A=36^{\circ}, \quad a=8, \quad b=5$$

Short Answer

Expert verified
Angle B measures approximately 55.96 degrees, angle C measures 88.04 degrees and the length of side c is approximately 10.89 units.

Step by step solution

01

Calculate angle B

Use the law of sines to find the unknown angle B. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides and angles. Plug in the values as follows: \(\frac{a}{\sin A} = \frac{b}{\sin B}\) Substituting our given values, \(\frac{8}{\sin 36} = \frac{5}{\sin B}\). Solving this equation yields \( \sin B = \frac{5\sin 36}{8}\). Finding the inverse sine of this answer gives the measure of angle B.
02

Calculate angle C

Since the sum of the angles in a triangle is 180 degrees, angle C can be calculated as such: \(C = 180 - A - B\). Plug in the known values and calculate to find the measure of angle C.
03

Calculate side c

Use the Law of Sines again but this time to find the length of side c. Rearranging the formula to find the side, use the equation: \(c = \sin C * \frac{a}{\sin A}\). Substituting the known values into the equation gives the length of side 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

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

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.) $$\tan (u-v)$$

Use the sum-to-product formulas to find the exact value of the expression. $$\sin 75^{\circ}+\sin 15^{\circ}$$

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

Verify the identity. $$\frac{\sin x \pm \sin y}{\cos x+\cos y}=\tan \frac{x \pm y}{2}$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Pure 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.