Question

In the given figure, find tan P and cot R is tan P=cot R?

Answer 1

SOLUTION :  

Given : Right angled ΔPQR, PQ = 12 cm & PR = 13 cm.  

Firstly find the remaining side (QR) of the triangle ΔPQR by using Pythagoras theorem (PR² = PQ² + RQ²),

In ΔPQR,  

PR² = PQ² + RQ²

13² = 12² + QR²

QR² = 13²  – 12²

QR² = 169 – 144

QR² = 25

QR = √25

QR = 5  

With reference to ∠P :  

tan P = Perpendicular Side Opposite To∠P/ Bass Side Adjacent to∠P

tan P = QR/ PQ

tan P = 5/12 …………………….(1)

With reference to ∠R:  

cot R=Base side adjacent to∠R / Perpendicular Side Opposite To∠R

cot R = QR/PQ

cot R = 5/12 ……………………..(2)

On Comparing equation (1) and (2), R.H.S of both the equation are equal.

Hence, L.H.S of both equations is also equal

tan P = cot R = 5/12

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

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