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easy

Law of Sines Problems - easy

Problem №1

Given a triangle ABC, in which $AB=\sqrt{2}$ and $\angle ACB=45^{\circ}$ , determine the length of the circumradius (radius of the circumscribed circle).

Solution:
By the law of sines, we have $\frac{AB}{\sin \angle ACB}=2R$ , so $R=\frac{AB}{2\sin\angle ACB}=\frac{\sqrt{2}}{2 \frac{\sqrt{2}}{2}}=1$

Problem №2

Given a triangle ABC, in which $AB=2\sqrt{3}$ and $\angle ACB=60^{\circ}$ , determine the length of the circumradius (radius of the circumscribed circle).

Solution:
By the law of sines, we have $\frac{AB}{\sin \angle ACB}=2R$ , so $R=\frac{AB}{2\sin\angle ACB}=\frac{2\sqrt{3}}{2 \frac{\sqrt{3}}{2}}=2$

Problem №3

Given a triangle ABC, in which $AB=5$ and $\angle ACB=30^{\circ}$ , determine the length of the circumradius (radius of the circumscribed circle).

Solution:
By the law of sines, we have $\frac{AB}{\sin \angle ACB}=2R$ , so $R=\frac{AB}{2\sin\angle ACB}=\frac{5}{2 \frac{1}{2}}=5$

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