To solve the given problem, we need to convert the angles from degrees and minutes to decimal degrees, then use the cosine function to find the cosine values, and finally multiply the results by 297.56.
Solution Approach
Convert the angles from degrees and minutes to decimal degrees.
Use the cosine function to find the cosine values of the converted angles.
Multiply the cosine values by 297.56.
Step 1: Convert Angles to Decimal Degrees
The angles given in degrees and minutes are converted to decimal degrees as follows:
Angle 1: 300∘5.3′=300+605.3≈300.0883∘Angle 2: 59∘54.7′=59+6054.7≈59.9117∘
Step 2: Calculate Cosine Values
Next, we calculate the cosine of the converted angles:
cos(300.0883∘)≈0.5013cos(59.9117∘)≈0.5013
Step 3: Multiply by 297.56
Finally, we multiply the cosine values by 297.56:
Result 1: 297.56⋅cos(300.0883∘)≈297.56⋅0.5013≈149.1771Result 2: 297.56⋅cos(59.9117∘)≈297.56⋅0.5013≈149.1771
Final Answer
The results for the calculations are:
149.1771
for both 297.56⋅cos(300∘5.3′) and 297.56⋅cos(59∘54.7′).