The previous topic explained how to find the trigonometric ratios.

This topic shows how to use them.

Solution of Right-angled Triangles

The sides and angles of right-angled triangles can be found using the trigonometric ratios. For each problem the information given should be written down and substituted into one of the ratios, which can then be solved as an equation.

Remember to use Pythagoras' Theorem if only sides are involved.

The final answer should be rounded off to a similar degree of accuracy to that given to measurements in the question.

Angles should be rounded to 1 decimal place.



Find the length of x




Using a calculator the step of writing out the value of cos 50°can be missed out:

Y9_Trigonometry_and_Triangles_03.gif Y9_Trigonometry_and_Triangles_04.gif Y9_Trigonometry_and_Triangles_05.gif Y9_Trigonometry_and_Triangles_06.gif Y9_Trigonometry_and_Triangles_07.gif Y9_Trigonometry_and_Triangles_08.gif 5.142300878 which rounds to 5.1

The difference in the two answers above is due to the rounding of cos 50° before multiplying by 8. The answers to 2 significant figures are the same.

Find the length of y



Using a calculator the step of writing out the value of sin 40°can be missed out:

Y9_Trigonometry_and_Triangles_11.gif Y9_Trigonometry_and_Triangles_12.gif Y9_Trigonometry_and_Triangles_13.gif Y9_Trigonometry_and_Triangles_14.gif Y9_Trigonometry_and_Triangles_07.gif Y9_Trigonometry_and_Triangles_08.gif 4.667171481 which rounds to 4.7

Find angle θ



On a calculator this last step is done as follows:

Y9_Trigonometry_and_Triangles_17.gif Y9_Trigonometry_and_Triangles_18.gif Y9_Trigonometry_and_Triangles_07.gif Y9_Trigonometry_and_Triangles_19.gif Y9_Trigonometry_and_Triangles_20.gif Y9_Trigonometry_and_Triangles_06.gif Y9_Trigonometry_and_Triangles_08.gif 36.86989765 which rounds to 36.9°