Question

In Fig below, Find tan P and cot R. Is tan P = cot R?

Answer 1

Let x be the adjacent side.

By Pythagoras theorem

𝑃𝑅² = 𝑃𝑄² + 𝑅𝑄²

169 = 𝑥² + 144

𝑥² = 25

𝑥 = 5

At LP, opposite side = 5

Adjacent side = 12

Hypotenuse = 13

`tan P = (1/12)/5 => 5/12`

At LR, opposite side = 12

Adjacent side = 5

Hypotenuse = 13

`cot R = 1/tan R = 1/(12/5) = 5/12`

`[∵ Tan R = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒"]`

∵ tan P = cot R