Express the following vertical angles as zenith distances 20

Express the following vertical angles as zenith distances: 20 degree 10\' -6 degree 20\' 60 degree 40\' -7 degree 10\'

Solution

Zenith distance = 90^o - vertical angle

a. Given vertical angle = 20^o10\' = (20 + 10/60) degrees (since 1\' = 1/60^o)

zenith distance = 90^o - (20 + 10/60)^o

= 89 + 60/60 -20 - 10/60

= (69 + 50/60) degree

zenith distance = 69^o50\'.............(Answer)

b. Given vertical angle = -6^o20\' = -(6 + 20/60) degrees (since 1\' = 1/60^o)

zenith distance = 90^o - (-(6 + 20/60))^o

= 90 + 6 + 20/60

= 96^o20\' degree

zenith distance = 96^o20\' .............(Answer)

c. Given vertical angle = 60^o40\' = (60 + 40/60) degrees (since 1\' = 1/60^o)

zenith distance = 90^o - (60 + 40/60)^o

= 89 + 60/60 -60 - 40/60

= (29 + 20/60) degree

zenith distance = 29^o20\'.............(Answer)

d. Given vertical angle = -7^o10\' = -(7 + 10/60) degrees (since 1\' = 1/60^o)

zenith distance = 90^o - (-(7 + 10/60))^o

= 90 + 7 + 10/60

= 97^o10\' degree

zenith distance = 97^o10\' .............(Answer)