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Maths

Trigonometry - Higher

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Finding an angle

Question

Find angle C. Give your answer correct to 1 dp.

image: triangle 2 sides given

Answer

We have been given the lengths of AC and BC and asked to find angle C.

  • AC is adjacent to angle C.
  • BC is the hypotenuse.
  • So we use the formula:
  • cos = adjacent / hypotenuse
  • cosC = 5/7
  • To calculate C we need to find the inverse of cos (INV cos or SHIFT cos):

    C = Inv cos(5/7)

    Using a calculator: C = 44.4°

Make sure that you know how your calculator works.

Use your calculator to find Inv cos(5/7), and check that you get the right answer (44.4°).

If you forget how to do it use this as a test:

The inverse cos of 1 is zero. Inv cos 1 = 0 (because cos0 = 1)

Question
image: triangle with 2 sides given

Find angle Z, giving your answer correct to 1 dp.

toggle answer

Answer

Z = 38.7°

You have been given the opposite and the hypotenuse. Therefore:

sin Z = 5/8

Z = inv sin(5/8)

Z = 38.7° (1 dp)

Questions involving trigonometry and right-angled triangles will only require you to know these three formula (sin, cos and tan). Make sure that you are confident with them.

Activity

Practise recognising the sides of a triangle, and calculating their lengths in this activity.

Now try a Test Bite

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