jugoslav

Let triangle ABC be the right-angled triangle with side lengths of 3, 4, and 5 units.

[DEF] / [ABC] = 13 / 30

Two angles of a triangle ABC measure 30 and 45 degrees. If the side of the triangle opposite the 30-degree angle measures 13 units, what is the sum of the lengths of the two remaining sides? Express your answer as a decimal to the nearest tenth.

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∠A = 30º        ∠B = 45º       a = 13

b + c = 43.499 units  

[ABC] = 180 square units

[DEF] = ¹/₄ [ABC]  = 45 square units

[DEF] : [ABC] = 1 : 4

∠ABC = tan^-1(AC / AB)

BC = sqrt(AB² + AC²) = √801

ΔABC inradius  r = 5.349

ΔABC circumradius   R = 14.151

Hello, Guest!

Your question is no good!!!            [ABC] cannot be more than 200 !!!

If [ABC] = 200 then the perimeter is 40 + 5√32  

JH = 12          JG = GK = 5

KH = sqrt(JG² + JH²) - GK         

KH = 8 units   

AC = BC = √50    |    AB = 10    |   CS = 5   |    AP = BQ

∠BCQ ≅ ∠ACP           ∠PCQ = 45º           ∠QCS = 22.5º

PQ = 2(tan∠QCS * CS)       PQ = 4.142135624

AP = BQ = 1/2(AB - PQ)      AP = BQ =  2.928932188

PQ² = 4.142135624² = 17.15728753

AP² + BQ² = 2.928932188² + 2.928932188² = 17.15728753

x = 65 degrees

Triangle AGD has an area of 150 square units.

Multiply 150 by 2, and divide the product by 25, and you'll have the radius.

 r = 300 / 25 = 12

Three circles fit inside a square as shown where two small circles touch a large circle. Given that the radius of the small circles is 3 and the side length of the square is 14, find the radius of the larger circle 

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Square side = 14             small radius r = 3             big radius R = ?

The distance between the centers of the small circles is 8 units.

So, we have       4² + (11 - R)² = (3 + R)²          R = 32 / 7    or   R ≈ 4.57 

The ratio is 2 : 1