Use a calculator to approximate each value in decimal degrees.
θ = arctan 1.7804675

Verified step by step guidance

1. Recognize that the problem asks for the angle \( \theta \) such that \( \tan(\theta) = 1.7804675 \). This means \( \theta = \arctan(1.7804675) \).
2. Recall that the arctangent function, \( \arctan(x) \), gives the angle whose tangent is \( x \), and the result is typically in radians or degrees depending on the calculator settings.
3. Set your calculator to degree mode since the problem asks for the angle in decimal degrees.
4. Use the calculator's arctangent function (often labeled as \( \tan^{-1} \) or \( \arctan \)) and input the value \( 1.7804675 \) to find \( \theta \).
5. The calculator will provide the approximate value of \( \theta \) in decimal degrees, which is the solution to the problem.

Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arctan, are used to find the angle whose trigonometric ratio equals a given value. For arctan, it returns the angle whose tangent is the input number, typically in radians or degrees.

Using a Calculator for Trigonometric Values

Calculators can compute inverse trigonometric functions directly, often requiring the mode to be set to degrees or radians. For arctan, input the value and use the arctan or tan⁻¹ function to find the angle.

Decimal Degrees

Decimal degrees express angles as a decimal number rather than degrees, minutes, and seconds. This format is useful for precise calculations and is commonly used in scientific and engineering contexts.