Question

Express 30°25'45" as a decimal of a right angle

With Explanation.
​

Answer 1

Given: 30° 25' 45"

To find: express the above angle as a decimal of a right angle

Solution:

• We know that, 60" = 1'
• Then 45" = (45/60)'
• = (3/4)'

• Now, 25' 45"
• = (25 + 3/4)'
• = (103/4)'

• We know that, 60' = 1°
• Then (103/4)' = (103/4 × 1/60)°
• = (103/240)°

• Now, 30° 25' 45"
• = (30 + 103/240)°
• = (7303/240)°

• We know that, 90° = 1 right angle
• Then, 1° = 1/90 of a right angle
• So, (7303/240)° = 1/90 × 7303/240
• = 0.3381 of a right angle

Answer: 30° 25' 45" is 0.3381 of a right angle.

Answer 2

Answer:

To find: express the above angle as a decimal of a right angle

Solution:

We know that, 60" = 1'

Then 45" = (45/60)'

= (3/4)'

Now, 25' 45"

= (25 + 3/4)'

= (103/4)'

We know that, 60' = 1°

Then (103/4)' = (103/4 × 1/60)°

= (103/240)°

Now, 30° 25' 45"

= (30 + 103/240)°

= (7303/240)°

We know that, 90° = 1 right angle

Then, 1° = 1/90 of a right angle

So, (7303/240)° = 1/90 × 7303/240

= 0.3381 of a right angle

Answer: 30° 25' 45" is 0.3381 of a right angle.

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