6 exam-style questions with full mark schemes and model answers. Write your own answer and the AI examiner marks it against the mark scheme.
Learn this properly: Angles and Angle ReasoningA cuboid storage crate PQRSTUVW has a rectangular base PQRS with PQ=9 cm and QR=12 cm. The crate stands upright, with vertex V directly above R and a vertical height RV=8 cm. The vertex P is the corner of the base diagonally opposite to R.
(a) Show that the diagonal PR of the base measures 15 cm. (2 marks)
(b) Work out the length of the space diagonal PV. (1 mark)
(c) Work out the angle that the space diagonal PV makes with the base PQRS, giving your answer to 1 decimal place. (2 marks)
In triangle LMN, the angle ∠MLN=40∘ and the angle ∠LMN=75∘. The side LN=14 cm.
(a) Find the size of angle ∠LNM. (1 mark)
(b) Work out the length of MN, giving your answer to 3 significant figures. (3 marks)
A triangular plot of land DEF has sides DE=8 m, EF=7 m and DF=9 m.
(a) Work out the size of the largest angle in the triangle, giving your answer to 1 decimal place. (3 marks)
(b) Hence work out the area of the plot, giving your answer to 3 significant figures. (1 mark)
A yacht sails in a straight line from harbour H to a marker buoy K, a distance of 26 km. The buoy K lies to the south-east of H: it is 24 km due east of H, and some distance due south of H. Work out how far south of H the buoy K is. (3 marks)
(a) Write down the exact value of cos60∘. (1 mark)
(b) A right-angled triangle has a side of length 5 cm adjacent to an angle of 60∘, and the right angle is at the foot of that side. Work out the exact length of the side opposite the 60∘ angle, giving your answer in the form a3. (1 mark)
A right-angled triangle has a side of length 5 cm opposite an angle θ, and the side adjacent to θ has length 7 cm. Work out the size of angle θ, giving your answer to 1 decimal place. (1 mark)