Use tables to find the acute angle θ, given that

(i) cos θ = .4625

(ii) cos θ = .9906

(iii) cos θ = .6951

(iv) cos θ = .3412

(i) Given,

cos θ = .4625
cos 62° 30' = .4617       (From tables)
Difference = .0008
Mean difference for 3' = .0008
θ = 62° 30' - 3' = 62° 27'.

Hence, the value of θ = 62° 27'.

(ii) Given,

cos θ = .9906
cos 7° 54' = .9905       (From tables)
Difference = .0001
Mean difference for 3' = .0001
θ = 7° 54' - 3' = 7° 51'.

Hence, the value of θ = 7° 51'.

(iii) Given,

cos θ = .6951
cos 46° 0' = .6947       (From tables)
Difference = .0004
Mean difference for 2' = .0004
θ = 46° 0' - 2' = 45° 58'.

Hence, the value of θ = 45° 58'.

(iv) Given,

cos θ = .3412
cos 70° 6' = .3404       (From tables)
Difference = .0008
Mean difference for 3' = .0008
θ = 70° 6' - 3' = 70° 3'.

Hence, the value of θ = 70° 3'.