A large triangle is shown with a vertical line of length y y\,y drawn from the top vertex to the base, creating a right angle. The left side of the triangle has a length of 10 cm and the right side has a length of 13 cm. The angle at the top-left vertex is 40∘40^\circ40∘. The angle at the bottom-right vertex is x∘x^\circx∘. The base of the triangle is divided into two segments; the right segment has a length of 5 cm.
Work out the value of xxx.
Give your answer to 1 decimal place.
The Cosine Rule Questions
Practise AQA GCSE Maths The Cosine Rule with exam-style questions for Foundation and Higher tier. 44 questions, matched to the AQA GCSE Maths (8300) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.