a^2 + b^2 = c^2
a = sqrt(c^2 - b^2) = sqrt (20^2 - 16^2)
= 12
sin[tex] \theta [/tex] = a/c = 12/20
= 3/5
cos[tex] \theta [/tex] = b/c = 16/20
= 4/5
tan[tex] \theta [/tex] = a/b = 12/16
= 3/4
csc[tex] \pi [/tex] = c/a = 20/12
= 5/3
= 1 2/3
sec[tex] \pi [/tex] = c/b = 20/16
= 5/4
= 1 1/4
The missing side of the right angle triangle is 12 .
The values of each of the six trigonometric ratios are as follows:
sin ∅ = 3 / 5
cos ∅ = 4 / 5
tan ∅ = 3 / 4
csc ∅ = 5 / 3
sec ∅ = 5 / 4
cot ∅ = 4 / 3
using Pythagoras's theorem,
c² = a² + b²
where
c = hypotenuse
a and b are the other legs
Therefore,
20² = a² + 16²
400 - 256 = a²
a² = 144
a = √144
a = 12
using trigonometric ratio,
sin ∅ = opposite / hypotenuse
cos ∅ = adjacent / hypotenuse
tan ∅ = opposite / adjacent
Therefore,
sin ∅ = 12 / 20 = 3 / 5
cos ∅ = 16 /20 = 4 / 5
tan ∅ = 12 / 16 = 3 / 4
csc ∅ = 1 / sin ∅ = 5 / 3
sec ∅ = 1 / cos ∅ = 5 / 4
cot ∅ = 1 / tan ∅ = 4 / 3
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