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.

Answer 1

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`