Using tables, find the acute angle θ, when:

(i) cos θ = 0.94

(ii) cos θ = 0.8092

(iii) cos θ = 0.1679

(i) Given,

cos θ = 0.94

cos 19° 54' = .9403

Difference = .0003

Mean difference of 3' = .0003

θ = 19° 54' + 3' = 19° 57'.

Hence, θ = 19° 57'.

(ii) Given,

cos θ = 0.8092

cos 35° 54' = .8100

Difference = .0008

Mean difference of 5' = .0008

θ = 35° 54' + 5' = 35° 59'.

Hence, θ = 35° 59'.

(iii) Given,

cos θ = 0.1679

cos 80° 18' = 0.1685

Difference = .0006

Mean difference of 2' = .0006

θ = 80° 18' + 2' = 80° 20'.

Hence, θ = 80° 20'.