/*! 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 70 Convert each angle to degrees-mi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 70

Convert each angle to degrees-minutes-seconds. Round to the nearest whole number of seconds. $$ 39.25^{\circ} $$

Short Answer

Expert verified
The angle is \( 39^{\text{\circ}} 15' 0'' \).

Step by step solution

01

Separate Degrees and Decimal

Identify the whole number part of the angle and the decimal part. For the angle \( 39.25^{\text{\circ}} \), the whole number part is 39 degrees and the decimal part is 0.25.
02

Convert Decimal to Minutes

Multiply the decimal part by 60 to convert it to minutes: \[ 0.25 \times 60 = 15 \text{ minutes} \]. So, 0.25 degrees is equal to 15 minutes.
03

Separate Minutes and Decimal

Since there is no further decimal in the minutes (it is exactly 15), we recognize that there are no seconds. Therefore, 15 minutes do not need further conversion.
04

Combine Results

Combine the degrees, minutes, and seconds to get the final result. The whole angle is \( 39^{\text{\circ}} 15' 0'' \).

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Angle Conversion
When dealing with angles, sometimes we need to switch between different formats. One common format is the degree-minute-second (DMS) system.
Degrees measure angles, where 1 degree equals 1/360th of a circle.
Sometimes, angles have decimals, and converting these to DMS is useful.
Each degree is split into 60 minutes, and each minute splits further into 60 seconds.
This conversion helps represent angles in a smaller, more precise format.
Trigonometry Basics
Trigonometry is the study of triangles, particularly the relationship between their angles and sides.
It's a crucial part of math, especially when working with angles.
Here are some key concepts:
  • Angles: Measured in degrees, which can be converted to minutes and seconds.
  • Triangles: The basis of trigonometry. Angles in a triangle always add up to 180 degrees.
  • Right-Angled Triangles: Used to define basic trigonometric functions (sine, cosine, and tangent).

Understanding these basics helps in grasping more complex trigonometric concepts and performing accurate calculations.
Decimal to Minutes Conversion
To convert a decimal part of a degree into minutes, follow a simple process.
First, identify the decimal part of the degree. In our example, it's 0.25.
Then, multiply that decimal by 60 (since 1 degree = 60 minutes).
For example:
  • 0.25 x 60 = 15 minutes.
This method allows converting any decimal degree into minutes and, if needed, into seconds if there's an additional decimal in the minutes.
Finally, combine the whole degrees with the minutes and seconds for the complete DMS form.

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

Solve each problem. In each case name the quadrant containing the terminal side of \(2 \alpha\) a. \(\alpha=66^{\circ}\) b. \(\alpha=2 \pi / 3\) c. \(\alpha=150^{\circ}\) d. \(\alpha=-5 \pi / 6\)

Use a calculator to find the value of each function. Round answers to four decimal places. $$ \sec \left(-9^{\circ} 4^{\prime} 7^{\prime \prime}\right) $$

Solve each problem. Spacing Between Teeth The length of an arc intercepted by a central angle of \(\theta\) radians in a circle of radius \(r\) is \(r \theta .\) The length of the chord, \(c\), joining the endpoints of that arc is given by \(c=r \sqrt{2-2 \cos \theta}\). Find the actual distance between the tips of two adjacent teeth on a 12 -in.-diameter carbide-tipped circular saw blade with 22 equally spaced teeth. Compare your answer with the length of a circular arc joining two adjacent teeth on a circle 12 in. in diameter. Round to the nearest thou- sandth.

Solve each problem. Throwing a Javelin The formula $$ d=\frac{1}{32} v_{0}^{2} \sin (2 \theta) $$ gives the distance \(d\) in feet that a projectile will travel when its launch angle is \(\theta\) and its initial velocity is \(v_{0}\) feet per second. Approximately what initial velocity in miles per hour does it take to throw a javelin \(367 \mathrm{ft}\) assuming that \(\theta\) is \(43^{\circ} ?\) Round to the nearest tenth.

Find the length of the arc intercepted by the given central angle \(\alpha\) in a circle of radius \(r\). Round to the nearest tenth. $$ \alpha=60^{\circ}, r=2 \mathrm{~m} $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Discrete 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.