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7.02 The sine rule

Interactive practice questions

Consider a triangle where all three sides are known, but no angles are known. Is there enough information to find all the angles in the triangle using only the sine rule?

A triangle with sides labeled as a, b, and c.

No

A

Yes

B
Easy
< 1min

Find the side length $a$a using the sine rule.

Round your answer to two decimal places.

Easy
2min

Find the value of the acute angle $x$x using the sine rule.

Round your answer to one decimal place.

Easy
3min

Find the value of the acute angle $x$x using the Sine Rule.

Write your answer in degrees correct to one decimal place.

Easy
2min
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Outcomes

4.2.1.3

establish and use the sine (ambiguous case is required) and cosine rules and the formula 𝐴rea=1/2 bc sin𝐴 for the area of a triangle

4.2.1.4

construct mathematical models using the sine and cosine rules in two- and three-dimensional contexts (including bearings in two-dimensional context) and use the model to solve problems; verify and evaluate the usefulness of the model using qualitative statements and quantitative analysis

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