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Question
In right angled ΔYXZ, ∠X = 90°, XZ = 8 cm, YZ = 17 cm, find sin Y, cos Y, tan Y, sin Z, cos Z, tan Z.
Solution
In right ∆YXZ,
YZ2 = XZ2 + XY2 ...(Pythagoras theorem)
⇒ XY2 = YZ2 − XZ2
⇒ XY2 = 172 − 82
⇒ XY2 = 289 − 64
⇒ XY2 = 225
⇒ XY2 = 152
∴ XY = 15 cm
Now,
sin Y = `("∠Y" "opposite side")/"Hypotenuse" = "XZ"/"YZ" = 8/17`
cos Y = `("∠Y" "adjacent side")/"Hypotenuse" = "XY"/"YZ" = 15/17`
tan Y = `("∠Y" "opposite side")/("∠Y" "adjacent side") = "XZ"/"XY" = 8/15`
Also,
sin Z = `("∠Z" "opposite side")/"Hypotenuse" = "XY"/"YZ" = 15/17`
cos Z = `("∠Z" "adjacent side")/"Hypotenuse" = "XZ"/"YZ" = 8/17`
tan Z = `("∠Z" "opposite side")/("∠Z" "adjacent side") = "XY"/"XZ" = 15/8`
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