SOHCAHTOA practice

Practice session

What you practise

Level 1: a side from an angle and the hypotenuse. Level 2: a side from an angle and one of the legs. Level 3: an angle from two sides. Level 4: everything mixed. Dutch classes call the rule SOS CAS TOA; the questions here use the English side names. The explanation and a calculator are on the SOHCAHTOA calculator page, and the SOHCAHTOA simulation shows what happens when the triangle grows.

Example

Find the opposite side when α = 30° and the hypotenuse is 10.

1. Opposite and hypotenuse: SOH.
2. opposite = hypotenuse · sin(α)
3. opposite = 10 · sin(30°) = 5

Answer: 5.

What you need to know

From the 2027 central exam syllabus. This is not a complete exam list; it is what you practice here.

havo · wiskunde B · subdomain C1 / vwo · wiskunde B · subdomain E1

Using sine, cosine and tangent to calculate angles and side lengths in a right triangle · sources syllabus wiskunde B havo 2027 (Examenblad), syllabus wiskunde B vwo 2027 (Examenblad)

• Point out the opposite and adjacent side from a given angle
• Choose the right ratio: SOH, CAH or TOA
• Work back to an angle with sin⁻¹, cos⁻¹ or tan⁻¹

vmbo · kader and gemengd/theoretisch · WI/K/6

The trigonometric ratios sine, cosine and tangent; in the gemengd/theoretisch track also in solids · source syllabus wiskunde vmbo 2027 (Examenblad)

• Calculator in degrees (DEG)
• Find a side when you know an angle and a side

Formula sheet

Print-friendly: use Print in your browser.

• SOH $$\sin \left(\alpha \right)=\frac{\text{opposite}}{\text{hypotenuse}}$$
• CAH $$\cos \left(\alpha \right)=\frac{\text{adjacent}}{\text{hypotenuse}}$$
• TOA $$\tan \left(\alpha \right)=\frac{\text{opposite}}{\text{adjacent}}$$
• Check: sin(30°) = 0,5 $$\sin (30°)=\mathrm{0,5}$$

Opposite side (overstaande zijde)

The leg that lies across from the angle you are working with.

Adjacent side (aanliggende zijde)

The leg that touches the angle you are working with (not the hypotenuse).

Practice with real exam questions on Examenblad.nl (in Dutch). We do not host past exams.

Frequently asked questions

What if my answer is only slightly different?

Sides count as correct within 0,02 and angles within 0,1°. So round the way the question says: sides to 2 decimal places, angles to 1 decimal place.

My answer is marked wrong, but I did everything right?

First check that your calculator is in degrees (DEG). In radians (RAD) you get different results.