Solving Right-Angled Triangles (Leaving Cert Mathematics): Quizzes

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Solving Right-Angled Triangles
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What does solving right-angled triangles mean?

Using trig ratios to find unknown sides/angles

What is the minimum information needed to solve a right-angled triangle?

Two pieces (one side & one angle, or 2 sides)

What is the sine ratio for angle θ\theta?

sin⁡θ=oppositehypotenuse\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}

What is the cosine ratio for angle θ\theta?

cos⁡θ=adjacenthypotenuse\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}

What is the tangent ratio for angle θ\theta?

tan⁡θ=oppositeadjacent\tan \theta = \frac{\text{opposite}}{\text{adjacent}}

In SOH-CAH-TOA, what does TOA represent?

Tangent = Opposite ÷ Adjacent

Which side is always the hypotenuse in a right-angled triangle?

The longest side, opposite the right angle

If you know the opposite and adjacent sides, which ratio finds the angle?

tan⁡−1\tan^{-1}

When do you use inverse trigonometric functions (sin⁡−1\sin^{-1}, cos⁡−1\cos^{-1}, tan⁡−1\tan^{-1})?

When you know two sides and want to find angle

What calculator mode must you use for these trigonometry problems?

Degree mode

To how many decimal places should you write trigonometric ratio values?

4 decimal places

If cos⁡32°=8x\cos 32° = \frac{8}{x}, how do you rearrange to find the hypotenuse xx?

x=8cos⁡32°x = \frac{8}{\cos 32°}

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