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this is the correct answer ok
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By Pythagoras theorem,
AC^2 = AD^2 + DC ^2
(13)^2 = AD^2 + (5)^2
169 = AD^2 + 25
AD^2 = 169 - 25
AD^2 = 144
AD = 12
(i) tan x = perpendicular/base
= CD/AD
= 5/12
Again by Pythagoras theorem,
AB^2 = AD^2 + BD^2
AB^2 = (12)^2 + (16)^2 {BD = BC - DC}
AB^2 = 144 + 256
AB^2 = 400
AB = 20
(ii) cos y = base/hypotenuse
= BD/AB
= 16/20
= 0.8
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