QuestionConvert the angle $\alpha=62^{\circ} 59^{\prime} 41^{\prime \prime}$ to decimal degrees.

Studdy Solution

STEP 1

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

STEP 2

First, we need to understand the relationship between degrees, minutes, and seconds.1 degree ( $^{\circ}$ ) is equal to60 minutes ( $^{\prime}$ ), and1 minute is equal to60 seconds ( $^{\prime \prime}$ ). Therefore,1 degree is equal to3600 seconds.

STEP 3

We can convert the minutes and seconds to degrees using the following formulas $Minutes\, in\, degrees = Minutes /60$ $Seconds\, in\, degrees = Seconds /3600$

STEP 4

Now, we plug in the given values for minutes and seconds to calculate their equivalent in degrees.
$Minutes\, in\, degrees =59 /60$ $Seconds\, in\, degrees =41 /3600$

STEP 5

Calculate the minutes and seconds in degrees.
$Minutes\, in\, degrees =59 /60 =0.9833\, degrees$ $Seconds\, in\, degrees =41 /3600 =0.0114\, degrees$

STEP 6

Now that we have the minutes and seconds in degrees, we can add these to the given degrees to find the total angle in decimal degrees.
$Decimal\, degrees = Degrees + Minutes\, in\, degrees + Seconds\, in\, degrees$

STEP 7

Plug in the values for the degrees, minutes in degrees, and seconds in degrees to calculate the total angle in decimal degrees.
$Decimal\, degrees =62 +0.9833 +0.0114$

STEP 8

Calculate the total angle in decimal degrees.
$Decimal\, degrees =62 +0.9833 +0.0114 =62.9947\, degrees$ The angle $\alpha=62^{\circ}59^{\prime}41^{\prime \prime}$ is approximately equal to $62.9947^{\circ}$ in decimal degrees.

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