Question

find the measurements of 4∠d + 3∠s where ∠d = 45° 32' 30" and ∠s = 25°15' 25"​

Answer 1

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.)