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Home > Maths I > Measure and Shape > Trigonometry

Maths I

Trigonometry

Using the trig ratio to calculate the size of an angle

Important. Set your calculator to 'degrees'.

Look at this sample question and guidance on how to answer it:

Calculate x^\circ.

A right angled triangle. The hypotenuse is labelled 10, the vertical edge is 8, and the shorter horizontal edge is not labelled. The angle between this and the hypotenuse is labelled x degrees.

First label the sides.

Form trig ratio:

sinx^\circ = \frac{opposite}{hypotenuse}

sinx^\circ = 8/10

Change ratio to a decimal number:

sinx^\circ = 0.8

Leave decimal number on the screen of your calculator. Key 'invsin' or '2fsin'.

Solution -

x^\circ = 53.1^\circ (to one decimal place)

Now try this one.

Question

Calculate\;x^\circ. Give your answer to one decimal place.

A right angled triangle. The hypotenuse is labelled 8, the shortest edge is 3, and the medium edge is not labelled. The angle between this and 8 is marked x degrees.
Answer

\;sin\;x^\circ = \frac{3}{8}

\;sin\;x^\circ = 0.375

\;x^\circ = 22.0^\circ(to one decimal place)

Use the same method in the following questions, but take care:

Sometimes you will use sinx^\circ, sometimes cosx^\circand sometimes tanx^\circ.

Hint: Show all working, especially when you use a calculator.

The examiner must see that you have understood the mathematics.

Question

Calculate\;x^\circ. Give your answer to one decimal place.

A right angled triangle. The hypotenuse is is labelled 12, the shortest edge is 7, and the medium edge is unlabelled. The angle between this and 12 is marked x degrees.
Answer

\;sin\;x^\circ= \frac{7}{12}

\;sin\;x^\circ= 0.5833...

\;x^\circ= 35.7^\circ

Question

Calculate\;x^\circ. Give your answer to one decimal place.

A right angled triangle. The hypotenuse is labelled 26, the horizontal edge is 20, and the vertical edge is not labelled. The angle between edges 20 and 26 is marked x degrees.
Answer

\;cos\;x^\circ= \frac{20}{26}

\;cos\;x^\circ= 0.769

\;x^\circ= 39.7^\circ

Question

Calculate\;x^\circ. Give your answer to one decimal place.

A right angled triangle. The edges coming off the right angle are labelled 2.6 and 4.8. The length of the hypotenuse is not given. The angle between the hypotenuse and edge 4.8 is marked x degrees.
Answer

\;tanx^\circ = \frac{2.6}{4.8}

\;tanx^\circ = 0.54166

x^\circ = 28.4^\circ

Question

Calculate\;x^\circ. Give your answer to one decimal place.

A right angled triangle. The hypotenuse is labelled 19, the medium edge is 14, and the length of the shortest edge is not given. The angle between edges 14 and 19 is marked x degrees.
Answer

\;cosx^\circ = \frac{14}{19}

\;cosx^\circ = 0.7368

x^\circ = 42.5^\circ

If you managed this you are doing really well. If you are still unsure, go over the questions again.

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