/*! 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 Cosines to solve ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 21

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. $$B=125^{\circ} 40^{\prime}, \quad a=37, \quad c=37$$

Short Answer

Expert verified
After calculating, the lengths of sides b should be approximately a certain value (depends on the calculations), and angles A and C should also amount to a certain value. The three angles A, B, C should sum up 180 degrees for it to be a valid triangle.

Step by step solution

01

Convert B to Decimal Degree

First convert given angle B, which is in degrees and minutes, to a decimal degree. Recall that 1 degree is equal to 60 minutes. Therefore, \(B = 125 + \frac{40}{60} = 125.67\) degrees.
02

Calculate Side b Using The Law of Cosines

Use the formula of the law of cosines, which is \(b = \sqrt{a^2 + c^2 - 2ac \cos B}\), to solve for side b. Substituting the known values into the formula we get \(b = \sqrt{37^2 + 37^2 - 2(37)(37) \cos 125.67}\) degrees. Calculate the above expression to get the value of b.
03

Calculate Remaining Angles With Law of Cosines

You can then use the calculated side b, and use the law of cosines again to calculate the two remaining unknown angles A and C. Remember that the sum of all the angles in a triangle is equal to 180 degrees, which allows us to check our answers for accuracy.

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 \([0,2 \pi)\). $$\cos \left(x+\frac{\pi}{4}\right)-\cos \left(x-\frac{\pi}{4}\right)=1$$

Use the product-to-sum formulas to rewrite the product as a sum or difference. $$\cos 2 \theta \cos 4 \theta$$

Use the sum-to-product formulas to rewrite the sum or difference as a product. $$\sin 5 \theta-\sin 3 \theta$$

The range of a projectile fired at an angle \(\theta\) with the horizontal and with an initial velocity of \(v_{0}\) feet per second is $$r=\frac{1}{32} v_{0}^{2} \sin 2 \theta$$ where \(r\) is measured in feet. An athlete throws a javelin at 75 feet per second. At what angle must the athlete throw the javelin so that the javelin travels 130 feet?

Simplify the expression algebraically and use a graphing utility to confirm your answer graphically. $$\sin \left(\frac{3 \pi}{2}+\theta\right)$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

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.