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Topic: It seems an easy problem, but I don't know how to solve it.?**Question:**
In triangle ABC:
AB=6
angle B=45degrees
angle C=30 degrees
therefore angle A=105degrees
But how do I find the semi-perimeter [ (a+b+c)/2 ] ?

June 16, 2019 / By Celeste

law of sines let a, and c, represent the lengths of the sides opposite the angles A, B , and C a / sin A = b / sin B = c / sin C and the reciprocals is true, too sin A / a = sin B / b = sin C /c AB = 6 is opposite angle C BC is opposite angle A AC is opposite angle B 6 / (sin 30º) = BC/ (sin (105º) = AC/sin (45º) 6/(1/2) = 12 12 = BC/sin (105º) = BC / (.9659) --> BC = 11.59 12 = AC/ sin (45º) = AC/ (√2/2) --> AC = 8.485 Now that you have the lengths, you can solve for the semiperimeter and I assume find the area of the triangle.

👍 236 | 👎 4

Did you like the answer? Well done to the first answer i'm pretty sure thats right. I've solved problems like this before and the hard bit is often not in solving equations, its about converting a real life problem into a mathematical problem. The confusing bit is deriving those two equations, but once you've got that sorted the rest is easy. Btw in case you don't have a fancy calculator handy: x² - 9x - 400 can be factorised as: (x-25)(x+16) giving x-25 = 0 x+16=0 x=25 x = -16 but we know the solution cannot be negative so only solution is x = 25 You can also complete the square: x² - 9x - 400 = 0 (x - 4.5)² - 20.25 - 400 = 0 (x- 4.5)² = 420.25 x - 4.5 = ±√420.25 x = 4.5 ± 20.5 x = 4.5 + 20.5 x = 4.5 - 20.5 x = 25 x = -16 so x must be 25 You can also use the quadratic formula: x = -b±√(b² - 4ac) /2a a=1 b=-9 c=-400 x = 9 ±√(81 +1600) /2 x = 9 ± 41 /2 x = 50/2 x = -32/2 x = 25 x = -16 nice to have options sometimes ;)

SOLUTION: Let 'y' be the total number of friends of Clara Number of pencils, 'x' = 400 Number of pencils for each friend of Clara, x = 400 / y ---> (1) Now, when 4 friends leave the group (means, y -4), then Each friend receives 5 more pencils (means, y - 4 = [x + 5] ----> (2) Substituting (1) in (2) => y - 4 = ( 400 / y ) + 5 => y -4 = [ 400 + 5y] / y => y (y - 4) = 400 + 5y => y^2 - 4y - 5y - 400 = 0 => y^2 - 9y - 400 = 0 taking factor => (y + 16) (y - 25) = 0 y - 25 = 0 => y = 25 Note: y + 16 = 0 will give 'y' as - 16, hence omitted.

b / sin 45° = 6 / sin 30° b = 6 sin 45° / sin 30° b = 6√2 a / sin 105° = 6 / sin 30° a = 6 sin 105 ° / sin 30° a = 3√6 + 3√2 P = 6 + 6√2 + 3√6 + 3√2 P = 6 + 3√6 + 9√2 P/2 = 3 + ( 3√6 + 9√2 ) / 2

👍 100 | 👎 -3

I am assuming AB is opposite angle C use sine formula 6/sinC = BC/sineA BC = 6sinA/sinC = 11.59.............correct to 2 decimal places AC/sinB = 6/sinC AC = 8.49..........................correct to 2 decimal places a + b + c = 26,08 Semiperimeter = 13.04

👍 97 | 👎 -10

Alright. 6x^3*7x^2-(4x^3)^2+(-3x^3)^2-(-4x^2)(5x^... right? (42x^5) - (16x^6) + (9x^9) - (-20x^5) - (10x^5) + (17x^6) (52x^5) - (x^6) + (9x^9) 9x^9 - x^6 + 52x^5 I think that is right.

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