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

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$\huge\tt{QUESTION\::-}$

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

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$\huge\tt{GIVEN\::-}$

• ∆PQR is a right angles triangle
• PQ = 7 cm
• PR = 25 cm

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$\huge\tt{TO\:FIND\::-}$

• tan P - tan R

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$\huge\tt{DIAGRAM\::-}$

$\setlength{\unitlength}{1.6cm}\begin{picture}(6,2)\linethickness{0.5mm}\put(7.7,2.9){\large\sf{P}}\put(7.7,1){\large\sf{Q}}\put(10.6,1){\large\sf{R}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(8.4,0.7){\sf{\large{}}}\put(7.4,2){\sf{\large{7 cm}}}\put(9.3,2){\sf{\large{25 cm}}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\put(9.4,1.2){\sf\large{^{} }}\end{picture}$

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$\huge\tt{SOLUTION\::-}$

• PQ = 7 cm (Given)
• PR = 25 cm (Given)

Bʏ Pʏᴛʜᴀɢᴏʀᴀs ᴛʜᴇᴏʀᴇᴍ

⇒ PR² = PQ² + QR²

⇒ 25² = 7² + QR²

⇒ QR² = 25² - 7²

⇒ QR² = 625 - 49

⇒ QR² = 576

⇒ QR = √576

⇒ QR = 24 cm

⇒ tan P = QR/PQ = 24/7

⇒ tan R = PQ/QR = 7/24

Here, We got tan P = 24/7 and tan R = 7/24

⇒ tan P - tan R

⇒ 24/7 - 7/24

⇒ (24)² - (7)² / 168

⇒ 576-49/168

⇒ 527/168

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