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CanadaON
Grade 12

Applications of the sine law

Interactive practice questions

Consider the given triangle.

A triangle with vertices labeled A, B, and C is presented. Vertex A is at the top, vertex B is on the lower left, and vertex C is on the lower right. The side opposite vertex A is labeled with the length of 18 units. The angle ABC at vertex B is labeled as 63 degrees, and the angle ACB at vertex C is labeled as 88 degrees, opposite to this angle is side AB labeled with lowercase letter '$c$c'.

a

First, find the value of $\angle BAC$BAC.

b

Find the length of $c$c.

Round your answer to two decimal places.

Easy
3min

Consider the following diagram:

Easy
3min

Use the sine rule to prove that the area of $\triangle ABC$ABC is given by the equation $Area=\frac{a^2\sin B\sin C}{2\sin A}$Area=a2sinBsinC2sinA.

Easy
3min

We want to prove that the area of a parallelogram is the product of two adjacent sides and the sine of the included angle.

Easy
2min
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Outcomes

12C.C.3.4

Solve problems involving oblique triangles, including those that arise from real-world applications, using the sine law (in non-ambiguous cases only) and the cosine law, and using metric or imperial units

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