ABC is an acute-angled triangle. BA=7cm and BC=8cm. The area of triangle ABC is 18 cm^2 . Work out the size of angle BAC. Give your answer correct to 3 significant figures. You must show all your working.
Draw the triangle ABC and fill in the information given i.e. lengths of BA and BC and identify the angle we are looking for i.e angle BAC Looking at the formulas given identify which one we can use. We have two sides and the area therefore the one we select is the Area of a Triangle i.e. Area=(1/2)(absinC). Substitute and rearrange to find angle ABC is equal to 40o Now we have two sides and an angle so we can use the Cosine Rule i.e. a2=b2+c2-2bccosA . Now substitute our values into that equation and take the positive square root to obtain AC is equal to 5.216cm Now we know we want to find the angle BAC so use the Sine Rule i.e. a/sinA=b/sinB. Substitute in the values and rearrange to obtain the the angle BAC is equal to 80.4o to 3 significant figures. This question was taken from the June 2016 Edexcel GCSE Higher Mathematics paper.
