Question

The sides of a right angled triangle PQR are PQ = 7 cm, PR = 25 cm and Q = 90°
respectively. Then find, tan P- tan R.
triangle ABC with right angle at B, in which a=24 units, b=25 units​

Answer 1

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