Quick questions on The sine rule, cosine rule and area of a triangle for HSC Maths Advanced: using the sine rule to find a side or an angle, the ambiguous (two-triangle) case of the sine rule, the cosine rule to find a side from SAS and an angle from SSS, and the area formula one half a b sin C, all in degrees with surveying and navigation contexts

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the area rule?

Show answer

The familiar area

= \tfrac12 \times \text{base} \times \text{height}

becomes, once you write the height as

a\sin C

(from the same dropped perpendicular as before),

What is the ambiguous case?

Show answer

This is the edge case textbooks flag and exams love. It happens only when you use the sine rule to find an angle, and never when you find a side or use the cosine rule. The reason is that two different angles share the same sine:

\sin\theta = \sin(180\degree - \theta)

. So

\sin B = 0.5

is satisfied by both

B = 30\degree

and

B = 150\degree

, and the sine rule cannot tell which one your triangle has.

What is calculator in radian mode?

Show answer

A triangle answer that is wildly wrong is almost always radians left on. Check

\sin 30\degree = 0.5

before starting, and keep degrees throughout.

Have a question we have not covered?

This dot-point answer is short enough that we have not extracted many short questions yet. Read the full dot-point answer or ask Mo, our study assistant, in the chat for follow ups.

All Maths AdvancedQ&A pages