/*! 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 54 A triangular parcel of land has ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 54

A triangular parcel of land has 115 meters of frontage, and the other boundaries have lengths of 76 meters and 92 meters. What angles does the frontage make with the two other boundaries?

Short Answer

Expert verified
The frontage makes one angle of \(C\) degrees and another angle of \(180 - C\) degrees with the two other boundaries.

Step by step solution

01

Using the Law of Cosines

To find the angles that the frontage makes with the other two boundaries, we'll first use the Law of Cosines. The formula for the Law of Cosines is: \[ c^{2} = a^{2} + b^{2} - 2ab\cos(C) \], where \(a\), \(b\) and \(c\) are the side lengths, and \(C\) is the angle we want to find. In this case, \(a = 76\) meters, \(b = 92\) meters, and \(c = 115\) meters. We'll start by finding \(\cos(C)\).
02

Calculate \(\cos(C)\)

Rearranging and solving for \(\cos(C)\) we get: \[ \cos(C) = (a^{2} + b^{2} - c^{2}) / 2ab \], Substitute the given values into the equation: \[ \cos(C) = (76^{2} + 92^{2} - 115^{2}) / 2*76*92 \] Calculate this to determine \(\cos(C)\).
03

Find angle \(C\)

To find the angle from the cosine, use the arccos (or inverse cosine) function. So \(C = \arccos(\cos(C))\). Remember to convert your answer to degrees if your calculator is in radian mode.
04

Find the other angle

To calculate the angle the frontage makes with the other boundary we'll use the property that the sum of the angles in a triangle is 180 degrees. So the other angle will be \(180 - C\).
05

Conclusion

The frontage makes one angle of \(C\) degrees and another angle of \(180 - C\) degrees with the two other boundaries.

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

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

Find all solutions of the equation in the interval \([0,2 \pi)\). $$\sin \left(x+\frac{\pi}{6}\right)-\sin \left(x-\frac{7 \pi}{6}\right)=\frac{\sqrt{3}}{2}$$

Use a graphing utility to approximate the solutions of the equation in the interval \([0,2 \pi)\). $$\tan (x+\pi)-\cos \left(x+\frac{\pi}{2}\right)=0$$

Determine whether the statement is true or false. Justify your answer. Complementary Angles If \(\phi\) and \(\theta\) are complementary angles, then show that (a) \(\sin (\phi-\theta)=\cos 2 \theta\) and \((\mathrm{b}) \cos (\phi-\theta)=\sin 2 \theta\).
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.