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Math  /  Geometry

Question85∘27′36′′−39∘5057′′=85^{\circ} 27^{\prime} 36^{\prime \prime}-39^{\circ} 5057^{\prime \prime}=

Studdy Solution

STEP 1

1. We are working with angles in degrees, minutes, and seconds.
2. 1∘=60′1^\circ = 60' (minutes) and 1′=60′′1' = 60'' (seconds).

STEP 2

1. Convert all angle measurements to a common unit.
2. Perform the subtraction.
3. Convert the result back to degrees, minutes, and seconds.

STEP 3

Convert 39∘5057′′39^\circ 5057'' to degrees, minutes, and seconds. First, convert the seconds to minutes and seconds:
5057′′=505760′=84′ remainder 17′′ 5057'' = \frac{5057}{60}' = 84' \text{ remainder } 17''
So, 39∘5057′′=39∘84′17′′39^\circ 5057'' = 39^\circ 84' 17''.

STEP 4

Align the two angles for subtraction:
85∘27′36′′ 85^\circ 27' 36'' −39∘84′17′′ -39^\circ 84' 17''

STEP 5

Since 27′<84′27' < 84', we need to borrow 1 degree from 85∘85^\circ to make it 84∘87′84^\circ 87':
84∘87′36′′ 84^\circ 87' 36'' −39∘84′17′′ -39^\circ 84' 17''

STEP 6

Subtract the seconds:
36′′−17′′=19′′ 36'' - 17'' = 19''

STEP 7

Subtract the minutes:
87′−84′=3′ 87' - 84' = 3'

STEP 8

Subtract the degrees:
84∘−39∘=45∘ 84^\circ - 39^\circ = 45^\circ
The result of the subtraction is:
45∘3′19′′ 45^\circ 3' 19''

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