Math, asked by TIYU23, 1 year ago

If in ∆ABC, with usaly rotation,a=18, b=24, c=30 then sinA/2=?

Answers

Answered by amitnrw
1

If in ∆ABC, with usaly rotation,a=18, b=24, c=30 then sinA/2= 1/√10

Step-by-step explanation:

Area of ∆ABC = (1/2) * b * c  * sinA

Area of Triangle using Hero Formula

s = (a + b + b)/2 = ( 18 + 24 + 30)/2

=> 36

Area = √s(s-a)(s-b)(s-c)

= √36 * 18 * 12 * 6

= 216

(1/2) * b * c  * sinA = 216

=> 24 * 30 * sinA = 432

=> sinA = 3/5

=> CosA = √1² - (3/5)²  = 4/5

CosA = 1 - 2Sin²(A/2)

=> 2Sin²(A/2) = 1 - CosA

=>  2Sin²(A/2)  = 1 - 4/5

=> 2Sin²(A/2)  = 1/5

=> Sin²(A/2) = 1/10

=> Sin(A/2) = 1/√10

Another Method

using Cosine formula

CosA  = (b² + c² - a²)/2bc

=> cosA = (24² + 30² - 18²)/(2 * 24 * 30)

=> CosA = 4/5

CosA = 1 - 2Sin²(A/2)

=> 2Sin²(A/2) = 1 - CosA

=>  2Sin²(A/2)  = 1 - 4/5

=> 2Sin²(A/2)  = 1/5

=> Sin²(A/2) = 1/10

=> Sin(A/2) = 1/√10

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