Perform each calculation. See Example 3. 90° ― 36° 18' 47"

Verified step by step guidance

1. Convert the angle 36° 18' 47" into decimal degrees. To do this, divide the minutes by 60 and the seconds by 3600, then add these to the degrees.
2. Calculate the decimal equivalent: 36 + (18/60) + (47/3600).
3. Subtract the decimal degree value obtained from 90°.
4. Perform the subtraction: 90° - (36 + (18/60) + (47/3600)).
5. Express the result in degrees, minutes, and seconds if needed by converting the decimal part back into minutes and seconds.

Key Concepts

Angle Measurement

Angles can be measured in degrees, minutes, and seconds, where 1 degree equals 60 minutes and 1 minute equals 60 seconds. This system allows for precise representation of angles, especially in trigonometry. Understanding how to convert between these units is essential for performing calculations involving angles.

Subtraction of Angles

Subtracting angles requires careful handling of degrees, minutes, and seconds. When subtracting, if the minutes or seconds of the second angle exceed those of the first, borrowing from the higher unit is necessary. This concept is crucial for ensuring accurate results in angle calculations.

Trigonometric Functions

Trigonometric functions such as sine, cosine, and tangent relate the angles of a triangle to the ratios of its sides. While the question focuses on angle subtraction, understanding these functions is vital for applying the results in broader trigonometric contexts, such as solving triangles or modeling periodic phenomena.