Question

In Fig. 5.37, find tan P and cot R. Is tan P = cot R?

Answer 1

Tan P = Cot R

Step-by-step explanation:

PQR is right-angled triangle. So PR² = PQ² + QR²

Given PR = 13cm and PQ = 12cm

13² = 12² + x²

169 - 144 = x²

 25 = x²

Therefore x = QR = 5cm

Tan p = QR/PQ = 5/12

Tan R = PQ/RQ = 12/5

Cot R = 5/12

So Tan P = Cot R

 Hence proved.

Answer 2

Given: ΔPQR is the right angled triangle where, PR =  13 cm and PQ = 12 cm.

To find: The values of tan P and cot R.

Applying Pythagoras theorem in ΔPQR to find the length of base QR, we get

PR² = PQ² + QR²

13² = 12² +  QR²

QR² = 13² - 12²

QR² = 169 - 144 = 25

QR = √25 = 5

QR = 5

Thus, the length of the base QR = 5 cm.

According to trignometric ratio,

tanP = Perpendicular side opposite to ∠P / Base side adjacent to ∠P

tanP = QR / PQ

tanP = 5/12  ..........(1)

And,

cot R = Base side adjacent to ∠R / Perpendicular side opposite to ∠R

cot R = QR / PQ

cot R = 5/12 ...............(2)

Comparing (1) and (2), we get

tan P = cot R

Thus, we see that tan P = cot R = 5/12