Questions: 246.46 * sin 8° 5.8′ =

246.46 * sin 8° 5.8′ =
Transcript text: $246,46 \cdot \sin 8^{\circ} 5,8^{\prime}=$
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Solution

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Solution Steps

To solve this problem, we need to calculate the sine of the given angle, which is in degrees and minutes, and then multiply it by the given number. First, convert the angle from degrees and minutes to decimal degrees. Then, use the sine function to find the sine of the angle. Finally, multiply the result by 246.46.

Step 1: Convert Angle to Decimal Degrees

The angle given is \( 8^{\circ} 5.8^{\prime} \). To convert this to decimal degrees, we use the formula: \[ \text{Decimal Degrees} = \text{Degrees} + \frac{\text{Minutes}}{60} \] Substituting the values: \[ \text{Decimal Degrees} = 8 + \frac{5.8}{60} = 8.096666666666666 \]

Step 2: Calculate the Sine of the Angle

Next, we calculate the sine of the angle in radians: \[ \sin(8.096666666666666^{\circ}) \approx 0.1408 \]

Step 3: Multiply by the Given Number

Now, we multiply the sine value by \( 246.46 \): \[ 246.46 \cdot 0.1408 \approx 34.7123 \]

Final Answer

The final result is approximately \( \boxed{34.7123} \).

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