/*! 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 14 Use a calculator to find each ra... [FREE SOLUTION] | 91影视

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Chapter 10: Problem 14

Use a calculator to find each ratio correct to four decimal places. $$\sin 27.5^{\circ}$$

Short Answer

Expert verified
\(\sin 27.5^{\circ} \approx 0.4620\)

Step by step solution

01

Set Up the Calculator

Ensure the calculator is in degree mode since the angle is given in degrees. Look for a 'DEG' indicator on display or set it to degrees in the settings.
02

Locate the Sine Function

Find and press the 'SIN' button on the calculator. This button is often denoted by 'sin'.
03

Input the Angle

Type in the angle value given in the problem, which is 27.5 degrees.
04

Calculate the Sine Ratio

Press the 'equals' button '=' or 'enter' to see the result. The calculator will display the sine of 27.5 degrees.
05

Round to Four Decimal Places

Round the result from the calculator to four decimal places. This is the final answer.

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Key Concepts

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

sine function
\(\text{sin 27.5^{\bullet}}\), it wants you to find this specific ratio. In calculators, the sine function is typically represented by the 'SIN' button. Using it, the calculator will compute the sine of the angle you provide.
using calculators
Calculators are incredibly helpful for solving trigonometric problems. Here is a simple guide: Ensure your calculator is turned on. Check if your calculator is in the correct mode (degree or radian). For this exercise, it should be in degree mode. Locate essential buttons: The 'SIN' button for the sine function, the numerical pad to input numbers, and the 'equals' button to get the result. Input the angle after pressing the 'SIN' button. Lastly, check the display screen for the result. Remember, practice helps in familiarizing with the calculator's functions.
degree mode
In trigonometry, angles can be measured in degrees or radians. For this particular exercise, the angle is given in degrees. Therefore, your calculator should be set to degree mode. Check if there's a 'DEG' or similar indicator on the display. If your calculator is in radian mode ('RAD' indicator), then switch it to degree mode. This setting can usually be adjusted in the calculator鈥檚 settings menu. Setting it correctly ensures accurate results when working with angles given in degrees.
rounding numbers
Rounding numbers is essential when presenting your final answer. The problem requires rounding the sine value to four decimal places. Follow these steps: Identify the fourth decimal place. Look at the digit immediately after the fourth decimal place. If it is 5 or greater, round the fourth decimal place up by one. If it's less than 5, keep the fourth decimal place the same. For instance, if the calculator shows a result of 0.462344, you will round it to 0.4623. Rounding ensures your answer is precise and easy to understand.

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Most popular questions from this chapter

Solve each right triangle in Exercises \(1-18 .\) Remember that \(m \angle C=90^{\circ} .\) Round to the same number of decimal places as in the given information. $$b=3.2 \text { and } m \angle B=10.8^{\circ}$$

A ship sails 30.0 miles in a direction of \(37.7^{\circ}\) west of due north. How far north has it sailed? How far west has it sailed? Round the answers to the nearest tenth of a mile.

Use a calculator to find the measure of \(\angle A,\) to the nearest tenth of a degree. $$\tan A=0.9301$$

Use a calculator to find each ratio correct to four decimal places. $$\tan 38^{\circ}$$

A chairlift at a ski resort makes an average angle of \(17.5^{\circ}\) with the horizontal ground at its base. If the vertical rise is 800 meters, what is the approximate length of the ride to the top of the lift?
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