Perform each calculation. See Example 3. 75° 15' + 83° 32'

Verified step by step guidance

1. Convert the angles from degrees and minutes to a more manageable form by separating the degrees and minutes.
2. Add the degrees together: 75° + 83°.
3. Add the minutes together: 15' + 32'.
4. If the sum of the minutes is 60 or more, convert the excess minutes into degrees (since 60 minutes = 1 degree) and add to the degrees.
5. Combine the final degrees and minutes to get the result.

Key Concepts

Degrees and Minutes

In trigonometry, angles can be measured in degrees and minutes, where one degree is divided into 60 minutes. This notation is often used for precision in angle measurement. For example, 75° 15' means 75 degrees and 15 minutes. Understanding how to convert between degrees and minutes is essential for performing calculations involving angles.

Angle Addition

Angle addition is a fundamental concept in trigonometry that involves combining two angles to find their sum. When adding angles expressed in degrees and minutes, it is important to add the degrees and minutes separately. If the sum of the minutes exceeds 60, it should be converted into degrees, which is a crucial step in ensuring accurate calculations.

Conversion of Minutes to Degrees

When performing calculations with angles, it is often necessary to convert minutes into degrees. Since 60 minutes equal 1 degree, any excess minutes after addition must be converted accordingly. For instance, if the total minutes exceed 60, you would convert every 60 minutes into 1 degree and add it to the total degrees. This conversion is vital for maintaining the integrity of the angle measurement.