How do you find an angle in a right-angled triangle?

Use \sin^{-1}, \cos^{-1} or \tan^{-1} of the ratio.

\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}

When do you use the sine rule?

When you know a side and its opposite angle, plus one other side or angle.

When do you use the cosine rule?

With two sides and the included angle, or with all three sides.

Area of a triangle using sine?

\frac12ab\sin C, where C is between sides a and b.

What does a negative cosine mean for a triangle angle?

The angle is obtuse (between 90^\circ and 180^\circ).

What is the first step in a trigonometry problem?

Sketch a well-labelled diagram and mark the known sides and angles.

How should you round in multi-step problems?

Keep full values and round only the final answer, to 3 significant figures.

3.2 Trigonometry in trianglesIB Maths: Applications and Interpretation HL: Flashcards

Card 1 of 130 of 13 known

Question

$\sin\theta$, $\cos\theta$, $\tan\theta$ in a right-angled triangle?

Tap or press Space to reveal

Tap card or press Space to flip

See all 13 cards

$\sin\theta$ , $\cos\theta$ , $\tan\theta$ in a right-angled triangle?: $\frac{\text{opp}}{\text{hyp}}$ , $\frac{\text{adj}}{\text{hyp}}$ , $\frac{\text{opp}}{\text{adj}}$
How do you find an angle in a right-angled triangle?: Use $\sin^{-1}$ , $\cos^{-1}$ or $\tan^{-1}$ of the ratio.
State the sine rule.: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$
When do you use the sine rule?: When you know a side and its opposite angle, plus one other side or angle.
State the cosine rule for a side.: $c^2=a^2+b^2-2ab\cos C$
State the cosine rule for an angle.: $\cos C=\frac{a^2+b^2-c^2}{2ab}$
When do you use the cosine rule?: With two sides and the included angle, or with all three sides.
Area of a triangle using sine?: $\frac12ab\sin C$ , where $C$ is between sides $a$ and $b$ .
What does a negative cosine mean for a triangle angle?: The angle is obtuse (between $90^\circ$ and $180^\circ$ ).
Which angle is opposite the longest side?: The largest angle.
Is the ambiguous case of the sine rule required at SL?: No.
What is the first step in a trigonometry problem?: Sketch a well-labelled diagram and mark the known sides and angles.
How should you round in multi-step problems?: Keep full values and round only the final answer, to 3 significant figures.

Exam questions on 3.2 Trigonometry in triangles

A wheelchair ramp is a straight slope of length 6 m that rises 0.9 m to a platform. The ground is horizontal.
A second ramp rises the same 0.9 m but is inclined at exactly $3^\circ$ to the horizontal. Find its length.2 marks
Two observers $P$ and $Q$ stand 120 m apart on level ground. A drone $D$ hovers in the vertical plane through $P$ and $Q$ , with $D\hat{P}Q=62^\circ$ and $D\hat{Q}P=48^\circ$ .
Find the distance $QD$ .2 marks
Two hikers leave a hut $H$ along straight paths that meet at an angle of $115^\circ$ . After some time, hiker $A$ is 3.5 km from $H$ and hiker $B$ is 5 km from $H$ .
Find the distance between the two hikers.3 marks

See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).