Trigonometric Ratios practice questions

Secondary 2 topics, working towards the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise trigonometric ratios free

What this topic covers

Finding Unknown Angles
Real-World Applications: Elevation, Depression and Heights
Trigonometric Ratios: SOH CAH TOA

Worked examples

Example 1

A tree is

16

m tall. A point on level ground is

30

m from the base of the tree. Find the angle of elevation from the point to the top of the tree, correct to the nearest degree.

Show the worked solution

$\tan \theta = \dfrac{\text{height}}{\text{distance}} \quad \scriptsize\textit{opposite over adjacent}$
$\tan \theta = \dfrac{16}{30}$
$\theta = \tan^{-1}\!\left(\dfrac{16}{30}\right) \quad \scriptsize\textit{inverse tan}$
$$\theta = 28°$ (to the nearest degree)$

Answer: $28$

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.