Questions: Find the acute angle A . - sin A=0.512 - A ≈ ° ′ (Round to the nearest minute as needed.)

Transcript text: Find the acute angle A . \[ \begin{array}{l} \sin A=0.512 \\ A \approx \square^{\circ} \square^{\prime} \end{array} \] (Round to the nearest minute as needed.)

Solution

Solution Steps

To find the acute angle \( A \) given \(\sin A = 0.512\), we need to use the inverse sine function (arcsin). After finding the angle in degrees, we will convert the decimal part of the degrees into minutes by multiplying it by 60 and rounding to the nearest minute.

Step 1: Calculate the Angle in Degrees

Given \(\sin A = 0.512\), we use the inverse sine function to find the angle \(A\): \[ A = \sin^{-1}(0.512) \approx 30.7971^\circ \]

Step 2: Separate Degrees and Decimal Part

Separate the integer part (degrees) and the decimal part: \[ \text{Degrees} = 30 \] \[ \text{Decimal Part} = 0.7971 \]

Step 3: Convert Decimal Part to Minutes

Convert the decimal part to minutes by multiplying by 60 and rounding to the nearest minute: \[ \text{Minutes} = 0.7971 \times 60 \approx 47.826 \approx 48 \]