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Chapter 10: Problem 12

Use a calculator to find each ratio correct to four decimal places. $$\tan 57.1^{\circ}$$

Short Answer

Expert verified
The tangent of 57.1 degrees is approximately 1.5402.

Step by step solution

01

Understand the Problem

The task is to find the tangent of an angle given in degrees and round it to four decimal places.
02

Set Up Your Calculator

Make sure the calculator is in degree mode. This is crucial because the given angle is in degrees.
03

Input the Value

Enter the angle value 57.1 degrees into the calculator.
04

Find the Tangent

Press the 'tan' button on the calculator to compute the tangent of 57.1 degrees.
05

Round to Four Decimal Places

Look at the result displayed on the calculator and round it to four decimal places. Ensure the fourth decimal place is accurate by checking the fifth decimal place for rounding.

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Key Concepts

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

tangent function
The tangent function is one of the primary trigonometric functions. It is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle. Given an angle \theta, the tangent is written as \(\tan(\theta)\). For example, if \theta is 57.1 degrees, we can find the ratio of the opposite side to the adjacent side using the tangent function. Understanding how to use the tangent function is crucial for solving various trigonometry problems.
degree mode
When dealing with angles, it is vital to set your calculator to the correct mode. There are generally two modes: degree mode and radian mode. Since the angle given in the exercise is in degrees, you must set your calculator to degree mode. This ensures the calculator interprets the angle correctly. To do this, look for a mode or settings button on your calculator and select 'DEG' or 'Degree'. This small but important step guarantees accurate results.
calculator usage
Using a calculator effectively can simplify solving trigonometric problems. Here are the steps:

1. **Check Mode:** Ensure it's in degree mode for this exercise.
2. **Enter the Angle:** Input the given angle, which is 57.1 degrees.
3. **Calculate:** Press the 'tan' button on the calculator.
4. **Read Result:** The calculator will display the tangent of 57.1 degrees. Make sure to follow these steps for a correct solution. Practicing these steps helps improve your efficiency and accuracy when using a calculator.
rounding decimals
Rounding decimals accurately is important in mathematics. For this exercise, rounding to four decimal places is required. Here's how you do it:

1. **Identify the Fourth Decimal Place:** Look at the fourth number after the decimal point.
2. **Check the Fifth Decimal Place:** This number determines whether you round up or keep the fourth decimal place as it is.
3. **Rounding Rules:**
  • If the fifth decimal place is 5 or greater, increase the fourth decimal place by one.
  • If it's less than 5, leave the fourth decimal place as it is.
This systematic approach ensures you get precise and reliable results.

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Most popular questions from this chapter

A forest ranger in a 100 -foot-tall fire tower sees a fire on the forest floor. The angle of depression from the tower to the fire is \(84^{\circ} .\) How far from the base of the tower is the forest fire?

Suppose, in a right triangle, the length of one leg and the measure of one acute angle are given. If you need to find the length of the hypotenuse, how do you decide which trigonometric ratio to use?

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?

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. \(a=6\) and \(b=8\)

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. $$a=19 \text { and } b=48$$
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