Question

The sides of a right angle triangle PQR are PQ = 7 cm PR = 25 cm and angle Q = 90° respectively. Then find Tan P - Tan R ?

Answer 1

tan p. = sine p / cos p
tan R = sine R / cos R

hypotnuse PR = 25cm
Side PQ= 7 cm
PR^2 = PQ^2 + QR^2
25^2 = 7^2 + QR^2
625 - 49 = QR^2
QR^2 = 576
QR = 24 cm

sin R = opposite side / hypotnuse
sin R = PQ/ PR
sin R = 7/ 25


cos R = adjacent side / hypotnuse
cos R = QR / hypotnuse
cos R = 24/25

sin p = opposite side / hypotnuse
sin p = QR / PR
sin p =24/25

cos p = adjacent side / hypotnuse
cos p = PQ/ PR
cos p = 7/25

tan p = sin p / cos p
tan p = (24/25)/ ( 7/25)
tan p = 24/7

tan R= sin R / cos R
tan R= (7/25)/ ( 24/ 25)
tan R = 7/24

tan p - Tan R = 24/7 - 7/24
tan p - tan r = 3.42 - 0.29
tan p - tan r = 3.13

Hope it helps you..

Answer 2

Hey mate !!

Here's the answer !!

Refer to the attachment for the diagram !!

Given that PQ = 7 cm, PR = 25 cm, ∠ Q = 90°.

Since it is a right angled triangle, we can find the other side of the triangle using Pythagoras Theorem.

In Δ PQR, PQ = Opposite side, PR = Hypotenuse, QR = Adjacent side.

Applying Pythagoras Theorem we get,

=> PR² = PQ² + QR²

=> PR² - PQ² = QR²

=> 25² - 7² = QR²

=> 625 - 49 = QR²

=> 576 = QR²

=> QR = √ 576

=> QR = 24 cm

Hence QR = 24 cm.

So Tan P = Opposite / Adjacent

Opposite side of ∠ P = QR, Adjacent side for ∠ P = PQ.

=> Tan P = QR / PQ

=> Tan P = 24 / 7


Tan R = Opposite / Adjacenet

Opposite side for ∠ R = PQ, Adjacent side for ∠ R = QR.

=> Tan R = PQ / QR

=> Tan R = 7 / 24

So Tan P - Tan R is,

=> 24 / 7 - 7 / 24

=> 3.42 - 0.29

=> 3.13

Hope my answer helped !!

Cheers !!