QuestionConvert the angle $\alpha=77.8211^{\circ}$ to degrees, minutes, and seconds.

Studdy Solution

STEP 1

Assumptions1. The given angle is in decimal degrees. We want to convert this angle to degrees, minutes, and seconds

STEP 2

First, we need to separate the degree part from the decimal part. The degree part is the integer part of the decimal degree.
$\alpha_{degree} = \lfloor \alpha \rfloor = \lfloor77.8211 \rfloor$

STEP 3

Calculate the degree part.
$\alpha_{degree} = \lfloor77.8211 \rfloor =77^{\circ}$

STEP 4

Next, we need to find the minute part. We do this by subtracting the degree part from the total angle and multiplying by60 (since there are60 minutes in a degree).
$\alpha_{minute} = (\alpha - \alpha_{degree}) \times60 = (77.8211 -77) \times60$

STEP 5

Calculate the minute part.
$\alpha_{minute} = (77.8211 -77) \times60 =49.266$

STEP 6

Again, we separate the integer part. This will be the minute part of the angle.
$\alpha_{minute} = \lfloor \alpha_{minute} \rfloor = \lfloor49.266 \rfloor$

STEP 7

Calculate the minute part.
$\alpha_{minute} = \lfloor49.266 \rfloor =49'$

STEP 8

Finally, we find the second part. We do this by subtracting the minute part from the total minutes (found in step5) and multiplying by60 (since there are60 seconds in a minute).
$\alpha_{second} = (\alpha_{minute} - \alpha_{minute}) \times60 = (49.266 -49) \times60$

STEP 9

Calculate the second part.
$\alpha_{second} = (49.266 -49) \times60 =15.96$

STEP 10

Round the second part to the nearest whole number.
$\alpha_{second} = \lfloor \alpha_{second} \rfloor = \lfloor15.96 \rfloor$

STEP 11

Calculate the second part.
$\alpha_{second} = \lfloor15.96 \rfloor =16''$ So, the angle $\alpha=77.821^{\circ}$ can be expressed as $77^{\circ}49'16''$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms