Use tables to find the acute angle θ, given that

(i) sin θ = .5789

(ii) sin θ = .9484

(iii) sin θ = .2357

(iv) sin θ = .6371

(i) Given,

sin θ = .5789
sin 35° 18' = .5779       (From tables)
Difference = .0010
Mean difference for 4' = .0010
θ = 35° 18' + 4' = 35° 22'.

Hence, the value of θ = 35° 22'.

(ii) Given,

sin θ = .9484
sin 71° 30' = .9483       (From tables)
Difference = .0001
Mean difference for 1' = .0001
θ = 71° 30' + 1' = 71° 31'.

Hence, the value of θ = 71° 31'.

(iii) Given,

sin θ = .2357
sin 13° 36' = .2351       (From tables)
Difference = .0006
Mean difference for 2' = .0006
θ = 13° 36' + 2' = 13° 38'.

Hence, the value of θ = 13° 38'.

(iv) Given,

sin θ = .6371
sin 39° 30' = .6361       (From tables)
Difference = .0010

Mean difference for 4' = .0009
and
Mean difference for 5' = .0011

Taking Mean difference for 4' = .0009
θ = 39° 30' + 4' = 39° 34'.

Hence, the value of θ = 39° 34'.