Convert the given angle to decimal degrees. Round to 4 decimal places. $$ 87^{\circ} 36^{\prime} 48^{\prime \prime} \approx $$

Question

UpStudy AI · Accepted Answer

1. Write the conversion formula:
$$
\text{Decimal Degrees} = \text{Degrees} + \frac{\text{Minutes}}{60} + \frac{\text{Seconds}}{3600}
$$

2. Substitute the given values:
$$
87^\circ + \frac{36^\prime}{60} + \frac{48^{\prime\prime}}{3600}
$$

3. Compute each term:
$$
\frac{36^\prime}{60} = 0.6,\quad \frac{48^{\prime\prime}}{3600} \approx 0.0133\overline{3}
$$

4. Sum the values:
$$
87 + 0.6 + 0.0133\overline{3} \approx 87.6133\overline{3}
$$

5. Round the result to four decimal places:
$$
87.6133^\circ
$$
The angle is approximately 87.6133 degrees.

Convert the given angle to decimal degrees. Round to 4 decimal places.