Ch. 2 - Acute Angles and Right Triangles

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. 2 - Acute Angles and Right Triangles

Problem 2.R.29

Chapter 3, Problem 2.R.29

Use a calculator to approximate the value of each expression. Give answers to six decimal places. tan 11.7689°

Verified step by step guidance

Recognize that the problem asks for the value of \(\tan 11.7689^\circ\), which means we need to find the tangent of the angle 11.7689 degrees.

Ensure your calculator is set to degree mode since the angle is given in degrees, not radians.

Input the angle 11.7689 into the calculator and then use the tangent function to find \(\tan(11.7689^\circ)\).

Calculate the value and then round or truncate the result to six decimal places as requested.

Write down the final answer with six decimal places, ensuring accuracy and proper formatting.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Understanding the Tangent Function

The tangent function relates an angle in a right triangle to the ratio of the opposite side over the adjacent side. It is defined for all angles except where cosine is zero, and its values can be positive or negative depending on the angle's quadrant.

Degree Measure and Angle Conversion

Angles can be measured in degrees or radians. In this problem, the angle is given in degrees, so it is important to ensure the calculator is set to degree mode to get the correct tangent value.

Using a Calculator for Trigonometric Approximations

Calculators can compute trigonometric functions to high precision. To approximate tan(11.7689°), input the angle in degree mode and round the result to six decimal places as required for accuracy.

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