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Home > Maths I > Measure and Shape > Trigonometry

Maths I

Trigonometry

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Using the trig ratio to calculate the length of a side

Now you are ready to use the trig ratio in a slightly different way.

Look at this example question and guidance on how to answer it

Calculate y.

Give your answer to two decimal places.

A right angled triangle. The hypotenuse is 12 centimetres, the shortest edge is y centimetres, and the medium edge is unlabelled. The angle between the two marked edges is 42 degrees.

Form the trig ratio:

cos42^\circ = \frac{y}{12}

Organise the equation:

12 \timescos42^\circ = y

Write the value of cos42^\circ:

12 \times 0.743... = y

Multiply and round as required:

8.92 = y (to two decimal places.)

Try these, using the same steps as the example above.

Question

Calculate\;y. Give your answer to three decimal places.

A right angled triangle. The hypotenuse is 12 centimetres, the shortest edge is y centimetres, and the medium edge is not labelled. The angle between this edge and the 12 centimetre one is 36 degrees.
Answer

\;sin36^\circ = \frac{y}{12}

\;12 \times\;sin36^\circ = y

12 \times 0.587... = y

7.053 (to three decimal places)

Question

Calculate\;y. Give your answer to three decimal places.

A right angled triangle. The edges coming from the right angle are labelled 7.5 centimetres and y metres. The hypotenuse is not labelled. The angle between the hypotenuse and 7.5 centimetres is 64 degrees
Answer

\;tan64^\circ = \frac{y}{7.5}

7.5 \times\;tan64^\circ = y

7.5 \times 2.050... = y

15.377 = y (to three decimal places)

Congratulations, you have completed all the trigonometry revision bite.

You are able to -

  • label sides
  • form a trig ratio
  • calculate the size of an angle
  • calculate the length of a side
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