Questions: Solve the right triangle B=72.7° (Round to the nearest tenth as needed.)

Solution Steps

To solve the right triangle given the angle \( B = 727^\circ \), we need to first convert the angle to a standard position within \( 0^\circ \) to \( 360^\circ \). Then, we can use trigonometric identities to find the missing sides or angles of the triangle.

1. Convert the given angle \( B = 727^\circ \) to an equivalent angle within \( 0^\circ \) to \( 360^\circ \).
2. Use trigonometric functions (sine, cosine, tangent) to solve for the missing sides or angles of the right triangle.
3. Round the results to the nearest tenth as needed.

Given the angle \( B = 727^\circ \), we convert it to an equivalent angle within the standard range of \( 0^\circ \) to \( 360^\circ \) using the modulo operation:

\[ B_{\text{standard}} = 727 \mod 360 = 7^\circ \]

Assuming we know the length of the adjacent side, which is given as \( \text{adjacent} = 5 \). We can find the length of the opposite side using the tangent function:

\[ \tan(B_{\text{standard}}) = \frac{\text{opposite}}{\text{adjacent}} \]

Rearranging gives us:

\[ \text{opposite} = \tan(7^\circ) \times \text{adjacent} \]

Calculating this, we find:

\[ \text{opposite} \approx \tan(7^\circ) \times 5 \approx 0.6139 \]

Rounding to four significant digits, we have:

\[ \text{opposite}_{\text{rounded}} \approx 0.6 \]

Final Answer