Pythagoras theorem with related questions

Trigonometry - 5

Hello friends ! Aaj k trigonometry -5 me mai aapko Pythgoras theorem k baare me bataunga. Saath hi saath iss theorem se related questions ko solve karna bhi shikhaunga.
Hello friends , Maths tricks in hindi me aapka ek baar phir swagat(welcome) karta hu.

Agar aap iss site par 1st baar visit kiya hai to mai aapko batadu ki , ye trigonometry tutorial ka 5th part hai. Agar aap part -1,2,3 and 4 read karna chhahte hai to maine iss post k last me link diya hai . Aap waha se read kar sakte hai.

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Aaj mai "Pythagoras theorem" k baare me aapko completely guide karunga. Ye theorem bahot hi jayada important hai. Iss theorem se related question ko kaise solve kiya jaata hai ?? Mai aapko details me bataunga.
Iss theorem ka use kark hum triangle k sides ko maalum karte hai.
Jab hum trigonometry k questions ko solve karte hai , tab hume iss theorem ki jarurat padati hai. Aaj hum issi topic k baare me details me jaanege. Aapka jyda time naa lete huye mai aaj ka part-5 start karta hu.

Pythagoras theorem with related questions

Iss theorem ko Pythagoras naam k ek mathematician ne diya. Isilye iss theorem ko inhi k naam par Pythagoras theorem kaha gaya.

Pythagoras , यूनान (Greece) k ek mahaan mathematician and philosopher the.
Aayiye ab mai aapko iss theorem k baare me batata hu.

Pythagoras theorem -:

Iss theorem k anusar , " kisi bhi right angle triangle (samkon tribhuj) me biggest arm(hypotenuse) ka square , other two small arms k square k sum k equal hota hai."

Iska matlab ye huya ki , samkon tribhuj k karn (hypotenuse) ka square , other two sides Aadhar(Base) aur lamb(height) k square k sum k equal hogi.

Also read-:
• 10 seconds me area of the triangle question solve
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For example -: Niche figure-1. me dekhiye.

Figure-1.

samkon ∆ABC me -:

Karn (Hypotenuse) = AC = c

Aadhar (Base) = AB = a

Lamb (height) = BC = b

Isliye according to the "Pythagoras theorem" -:

(Karn)² = (Lamb)² + (Aadhar)²

AC² = AB² + BC²

"Pythagoras theorem" se related questions

Q-1.-: ∆ABC me /_B = 90°, BC = 10, AB = 24 ho to karn(Hypotenuse) gyat kijiye .

Sol-: Sabse pahle hum iss question k according figure banate hai. Maine niche image me figure diya hai.

Figure me diya hai -:
AB = 24 , BC = 10 aur AC = ??
Ab hum Pythagoras theorem use karte hai-:
AC² = AB²+BC²
= (24)²+(10)²
= 576+100
= 676
Isliye AC = √676
= 26
karn(Hypotenuse) AC = 26 Answer.

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Q-2.-: Figure ki help se Lamb ( height ) BC gyat kijiye.

Sol-: AB = 12 aur AC = 13 , hume BC maalum karna hai.
Isliye Pythagoras theorem k formula ko change karne par -:
BC² = AC² - AB²
= (13)²-(12)²
= 169 - 144
= 25
Tab , BC = √25
= 5
Lamb ( height ) BC = 5 Ans.

Q-3.-: Figure ki help se Aadhar ( Base ) ki value batayiye.

Sol-: AC = 5 aur BC = 4 tab AB = ??
According to Pythagoras theorem-:
AB² = AC² - BC²
= (5)²-(4)²
= 25 - 16
= 9
Tab , AB = √9
= 3
Aadhar ( Base ) AB = 3 Ans.

Q-4.-: Yadi sin A = 8/10 , to cos A ka maan gyat kijiye.

Sol-: Diya hai ki sinA = 8/10
hum jaante hai ki
sinA = lamb/karn
Matlab lamb BC = 8 aur karn AC = 10 diya hai. Hume Adhar AB calculate karna hai.
According to Pythagoras theorem-:
AB² = AC² - BC²
= (10)²-(8)²
= 100 - 64
= 36
Tab , AB = √36
= 6
Aadhar ( Base ) AB = 6
cos A = Aadhar/karn
= AB/AC
= 6/10
= 3/5 Answer.

Q-5.-: Yadi tan A = 1/√2, ho to cosecA ki value kya hogi ?

Sol-: tanA = L/A = 1/√2
BC = 1 aur AB = √2 , AC = ??
According to Pythagoras theorem-:
AC² = AB² + BC²
= (√2)²+(1)²
= 2+1
= 3
Tab , AC = √3
cosecA = K/L
= AC/BC
= √3/1
= √3
cosecA ki value = √3 Ans.

Q-6.-: Agar cosA = 2/3 ho to tanA×cosA = ??

Sol-: cos A = A/K = 2/3
Means , AB = 2 aur AC = 3 , BC = ??
According to Pythagoras theorem-:
BC² = AC² - AB²
= (3)²-(2)²
= 9 - 4
= 5
Tab , BC = √5
tanA = L/A
= BC/AB
= √5/2
tanA×cosA = √5/2 × 2/3
= √5/3 Ans.

Q-7.-: Kisi triangle me cotA = 1/√3 ho to "√3(secA - cotA)" ka maan batayiye.

Sol-: cot A = 1√3 , hum jaante hai ki, cotA = Aadhar(AB) / lamb(BC)
Matlab question me diya hai -:
AB = 1 aur BC = √3
Hume karn(AC) calculate karna hai .
AC = ??
According to Pythagoras theorem-:
AC² = AB² + BC²
= (1)²+(√3)²
= 1+3
= 4
Tab , AC = √4 = 2
secA = Karn/Aadhar
= AC/AB
= 2/1
= 2
√3(secA - cotA) = √3(2 - 1/√3)
= 2√3 - 1 Ans.

Q-8.-: Yadi tan A = 5/6 ho to gyat kijiye-:

   tanA+secA
tanA - secA

Sol-: tanA = L/A = 5/6
Means , BC = 5 aur AB = 6 , AC = ??
According to Pythagoras theorem-:
AC² = AB² + BC²
= (6)²+(5)²
= 36+25
= 61
Tab , AC = √61
secA = K/A
= AC/AB
= √61/6
   tanA+secA
tanA - secA
= 5/6 + √61/6
5/6 - √61/6
Solve karne k baad -:
= 5+√61
5-√61 Answer.

Q-9.-: Yadi sec A = 2 ho to nimnlikhit ka maan gyat kijiye -:

sinA
1+cosecA

Sol-: secA = karn/Aadhar = 2/1
Means, AC = 2 and AB = 1 , BC = ??
According to Pythagoras theorem-:
BC² = AC² - AB²
= (2)²-(1)²
= 4 - 1
= 3
Tab , BC = √3
Aadhar ( Base ) AB = √3
sinA = lamb/karn
= BC/AC
= √3/2
cosec A = karn/lamb
= AC/BC
= 2/√3
    sinA
1+cosecA
= √3/2
1+ 2/√3
Simplify karne k baad -:
= 3/2(√3+2) Ans.

Q-10.-: Yadi cosec A = 2/√3 ho to secA + cotA = ??

Sol-: cosec A = 2/√3
Hum jaante hai ki, cosec A = karn/lamb
Matalab , karn AC = 2 aur lamb BC = √3
Aadhar AB = ??
According to Pythagoras theorem-:
AB² = AC² - BC²
= (2)²-(√3)²
= 4 - 3
= 1
Tab , AB = √1
= 1
Aadhar ( Base ) AB = 1
SecA = Karn/Aadhar
= AC/AB
= 2/1
= 2
cotA = Aadhar/lamb
= AB/BC
= 1/√3
Isliye, secA + cotA = 2+ 1/√3
= (2√3+1)/√3 Ans.

Trigonometry tutorial k iss part me bas itana hi . Ab iss k aage, hum next post me shikhenge .
Aapko aaj k topic me koi problem huyi ho to , aap comment kark pucch sakte hai.Agar aapko aaj ka topic pasand aaya to please share kare.

Trigonometry se related topics ki important link -:

1. Trigonometry ka basic concept in hindi part-1
2. Triangle and its types and defination in hindi part - 2
3. Basic of trigonometric ratio part- 3
4. Trigonometric ratio se related Questions with solutions part - 4