Use tables to find the acute angle θ, given that

(i) tan θ = .2685

(ii) tan θ = 1.7451

(iii) tan θ = 3.1749

(iv) tan θ = .9347

(i) Given,

tan θ = .2685
tan 15° 0' = .2679       (From tables)
Difference = .0006
Mean difference for 2' = .0006
θ = 15° 0' + 2' = 15° 2'

Hence, the value of θ = 15° 2'.

(ii) Given,

tan θ = 1.7451
tan 60° 6' = 1.7391       (From tables)
Difference = .0060
Mean difference for 5' = .0060
θ = 60° 6' + 5' = 60° 11'

Hence, the value of θ = 60° 11'.

(iii) Given,

tan θ = 3.1749
tan 72° 30' = 3.1716       (From tables)
Difference = .0033
Mean difference for 1' = .0033
θ = 72° 30' + 1' = 72° 31'

Hence, the value of θ = 72° 31'.

(iv) Given,

tan θ = .9347
tan 43° 0' = .9325       (From tables)
Difference = .0022
Mean difference for 4' = .0022
θ = 43° 0' + 4' = 43° 4'

Hence, the value of θ = 43° 4'.