Trigonometry · Ordinary Level

Exam-Style Problems

Ordinary Level · Class 11 · Tap NEXT to begin

Section 1 of 2

Putting It Together

Read carefully

Exam questions mix the rules. Sketch the triangle, mark what you know, then choose: right angle → SOH CAH TOA; a pair → Sine Rule; two sides and the angle between → Cosine Rule.

Worked example — Olga measures a distance

Olga marks a point $P$ so that $|RP| = 20\,\text{m}$. She measures $|\angle ORP| = 88^\circ$ and $|\angle ORP\text{ at }P| = 87^\circ$. Work out $|OR|$ to the nearest metre.

Third angle at $O = 180 - (88 + 87) = 5^\circ$

$|OR|$ faces the $87^\circ$; $|RP| = 20$ faces the $5^\circ$

$\dfrac{|OR|}{\sin 87} = \dfrac{20}{\sin 5} \Rightarrow |OR| = \dfrac{20\sin 87}{\sin 5} = 229\,\text{m}$

$|OR| = 229\,\text{m}$

Section 2 of 2

A Full Exam Question

A garden is divided into parts. $|PR| = 3.3\,\text{m}$, $|PQ| = 6.5\,\text{m}$, $|QS| = 8\,\text{m}$, $|\angle QRP| = 90^\circ$, $|\angle PQR| = \alpha$ and $|\angle RQS| = \beta$.

Worked example — (a) Pythagoras

Find $|RQ|$.

$\triangle PQR$ is right-angled at $R$: $|PR|^2 + |RQ|^2 = |PQ|^2$

$3.3^2 + |RQ|^2 = 6.5^2 \Rightarrow |RQ|^2 = 42.25 - 10.89 = 31.36$

$|RQ| = 5.6\,\text{m}$

Worked example — (b) show α = 31°

Show that $\alpha = 31^\circ$ to the nearest degree.

At $Q$: opposite $= |PR| = 3.3$, hypotenuse $= |PQ| = 6.5$ $\Rightarrow$ $\sin$

$\sin \alpha = \dfrac{3.3}{6.5} \Rightarrow \alpha = 30.5 = 31^\circ$

$\alpha = 31^\circ$

Worked example — (c) find β

Use $\alpha = 31^\circ$ to find $\beta$.

$\angle RQS$ and $\angle PQR$ sit on a straight line, so $\beta = 180 - 31 = 149^\circ$

$\beta = 149^\circ$

You try

(d) Use the Cosine Rule to find $|RS|$, correct to the nearest metre. Use $|RQ| = 5.6$, $|QS| = 8$ and $\beta = 149^\circ$.

$|RS|^2 = 5.6^2 + 8^2 - 2(5.6)(8)\cos 149$.

$|RS|^2 = 31.36 + 64 - 89.6\cos 149 = 172.16$

$|RS| = 13.1 = 13\,\text{m}$

$|RS| = 13\,\text{m}$

That’s Trigonometry — the last class!

You’ve covered right-angled trig, elevation & depression, the Sine Rule, the Cosine Rule and area. Climb the rest of the pyramid to lock it in.