Q3. Find the measurements of 42D + 32S
where 2D = 45° 32' 30" and
25 = 25°15' 25"
Answers
Question :- find the measurements of 4∠d + 3∠s where ∠d = 45° 32' 30" and ∠s = 25°15' 25" . ?
Solution :-
we know that,
- 1° = 60' => 1 degree = 60 minutes .
- 1' = 60'' => 1 minute = 60 seconds .
so,
- 1' = (1/60°)
- 1'' = (1/60)' => (1/60 * 60)°
so,
→ ∠d = 45° 32' 30"
→ ∠d = 45° + (32/60)° + (30/60*60)°
→ ∠d = 45° + (8/15)° + (1/120)°
→ ∠d = {(45*120 + 8*8 + 1)/120}°
→ ∠d = {(5400 + 64 + 1)/120}°
→ ∠d = (5465/120)°
similarly,
→ ∠s = 25°15' 25"
→ ∠s = 25° + (15/60)° + (25/60*60)°
→ ∠s = 25° + (1/4)° + (1/144)°
→ ∠s = {(25*144 + 1*36 + 1)/144}°
→ ∠s = {(3600 + 36 + 1)/144}°
→ ∠s = (3637/144)°
therefore,
→ 4∠d + 3∠s
→ 4(5465/120)° + 3(3637/144)°
→ (5465/30)° + (3637/48)°
→ [(5465 * 8 + 3637 * 5)/240]
→ (43720 + 18185) / 240
→ (61905/240)°
→ 257(225/240)°
→ 257(15/16)°
→ 257°[(15/16) * 60]'
→ 257°[(15 * 15/4)]'
→ 257°(225/4)'
→ 257°56'(1/4)'
→ 257°56'(1/4 * 60)''
→ 257°56'15'' (Ans.)