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Sine Rule Problems

Problem 1 In the ABC we have AB = 30cm and γ = 45°. Find the length of the radius of the perscribed circumference.
Answer: 15√2cm.

Problem 2 The radius of the perscribed around ABC circumference is R = 2√3/3cm. Find the size of the angle α, if BC = 2cm.
Answer: 60°.

Problem 3 In the ABC α : β : γ = 1 : 3: 8. Find the length if the side AC, if AB = 10cm.
Answer: 10√63cm.

Problem 4 In the circumference with radius 7cm, the arc AB is 120°. Find the chord AB.
Answer: 7√3cm.

Problem 5 In the isosceles triangle ABC, the base AB = 12cm, and the angle at the top is 30°. On the hip BC is taken point D so that CAD : DAB = 1 : 4. Find the length of the radius of the perscribed circumference around the ABD.
Answer: 6√2cm.

Problem 6 The base of isosceeles triangle is 10cm, and the anlge at the base is 2α. Find the bisectrice of the angle at the base.
Angle: 10sin2α/sin3α.

Problem 7 In the ABC we have AB = 12cm and γ = 60°. Find the radius of the perscribed around the ABL circumference, if the point L is the L intersect of the bisectrices of ABC.
Answer: 4√3cm.

Problem 8 In the circumference with radius 50cm is inscribed quadrilateral. Two if its angles are 45° and 120°. Find the diagonales.
Answer: 50√2cm or 50√3cm.

Problem 9 In ABC we have α = 45°, β = 30°. On the side AB we is chosen point M. The radius of the perscribed around the AMC circumference is R. Find the radius of the perscribed around the MBC circumference.
Answer: R√2cm.