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Question
In ΔPQR, right angled at Q, PQ = 4 cm and RQ = 3 cm. Find the values of sin P, sin R, sec P and sec R.
Solution
ΔPQR right angled at Q.
Let x be the hypotenuse
By applying Pythagoras
𝑃𝑅2 = 𝑃𝑄2 + 𝑄𝑅2
𝑥2 = 42 + 32
𝑥2 = 16 + 9
`∴ x = sqrt25 = 5`
Find sin 𝑃 , sin 𝑅, sec 𝑃, sec 𝑅
At LP, opposite side = 3 cm
Adjacent side = 4 cm
Hypotenuse = 5
`sin P = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒" = 3/5`
`sec P = "𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒"/"𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒" = 5/4`
At LK, opposite side = 4 cm
Adjacent side = 3 cm
Hypotenuse = 5 cm
`sin R = 4/5`
`sec R = 5/3`
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