The previous topic explained how to find the trigonometric ratios.
This topic shows how to use them.
Solution of Rightangled Triangles
The sides and angles of rightangled 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: 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: 4.667171481 which rounds to 4.7 

Find angle θ 

On a calculator this last step is done as follows: 36.86989765 which rounds to 36.9° 