Questions: cos 43.15 = (2b / 24.2) / (b = 29.2 × cos(43.15))

Solution Steps

The given text seems to contain two separate mathematical expressions. Let's address the first one, which is a simple arithmetic operation. The second expression appears to be a trigonometric equation involving cosine, which can be solved for \( b \).

1. Arithmetic Operation: Subtract 0.158 from 4.
2. Trigonometric Equation: Solve the equation \(\frac{\cos 43.15 = \frac{2b}{24.2}}{b = 29.2 \times \cos(43.15)}\) for \( b \).

To solve the arithmetic operation, we subtract \(0.158\) from \(4\):

\[ 4 - 0.158 = 3.842 \]

The trigonometric equation given is:

\[ \frac{\cos 43.15 = \frac{2b}{24.2}}{b = 29.2 \times \cos(43.15)} \]

First, calculate \(\cos(43.15^\circ)\):

\[ \cos(43.15^\circ) \approx 0.7296 \]

Using this value, solve for \(b\):

\[ b = 29.2 \times 0.7296 \approx 21.30 \]

Final Answer