Quick questions on Trigonometric ratios in right-angled triangles explained: N(A)-Level Mathematics Mensuration and Trigonometry

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are labelling the sides?

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For a chosen angle (not the right angle), the three sides are named relative to it:

What are the three ratios?

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The ratios connect the angle to two of the sides:

What is finding a side?

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To find a missing side: label the sides, pick the ratio that uses the two sides you care about, substitute, and rearrange. For a

40^\circ

angle with hypotenuse

12

, finding the opposite uses sine:

\text{opposite} = 12 \sin 40^\circ

What is finding an angle?

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To find a missing angle: form the ratio from the two known sides, then use the inverse function (

\sin^{-1}

\cos^{-1}

\tan^{-1}

) on the calculator. If

\tan \theta = \dfrac{3}{4}

, then

\theta = \tan^{-1}\!\left(\dfrac{3}{4}\right) = 36.9^\circ

What is calculator in the wrong mode?

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It must be in degrees, not radians, for this syllabus.

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