Questions: 381.45 * cos 13° 1.4' =

381.45 * cos 13° 1.4' =
Transcript text: $381,45 \cdot \cos 13^{\circ} 1,4^{\prime}=$
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Solution

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Solution Steps

To solve this problem, we need to calculate the cosine of the given angle and then multiply it by the given number. The angle is given in degrees and minutes, so we first convert it entirely into degrees. Then, we use the cosine function to find the cosine of the angle and multiply the result by 381.45.

Step 1: Convert Angle to Degrees

The angle given is \( 13^{\circ} 1.4^{\prime} \). To convert this to decimal degrees, we use the formula: \[ \text{angle in degrees} = 13 + \frac{1.4}{60} = 13.0233 \]

Step 2: Calculate Cosine of the Angle

Next, we calculate the cosine of the angle: \[ \cos(13.0233^{\circ}) \approx 0.9743 \]

Step 3: Multiply by the Given Number

Now, we multiply the cosine value by the given number \( 381.45 \): \[ \text{result} = 381.45 \cdot 0.9743 \approx 371.6385 \]

Final Answer

The final result is approximately: \[ \boxed{371.6385} \]

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