Edexcel GCSE Maths: Pythagoras and Trigonometry

In triangle $ABC$ABC, $AB = 9.4$AB=9.4 cm, $BC = 7.1$BC=7.1 cm and angle $ABC = 124^{\circ}$ABC=124∘.

(a) Work out the length of $AC$AC, giving your answer correct to 3 significant figures. (3 marks)

(b) Work out the area of triangle $ABC$ABC, giving your answer correct to 3 significant figures. (2 marks)

A right-angled triangle has a hypotenuse of length $13$13 cm. One of the other two sides has length $5$5 cm.

(a) Work out the length of the third side. (2 marks)

(b) Work out the size of the smallest angle in the triangle, giving your answer correct to 1 decimal place. (2 marks)

A boat sails from a harbour $H$H on a bearing of $062^{\circ}$062∘ for $8$8 km to a buoy $B$B. It then sails on a bearing of $152^{\circ}$152∘ for $6$6 km to a point $C$C.

(a) Explain why angle $HBC = 90^{\circ}$HBC=90∘. (1 mark)

(b) Work out the direct distance $HC$HC. (3 marks)

A ladder leans against a vertical wall. The foot of the ladder is $1.8$1.8 m from the base of the wall on horizontal ground, and the ladder makes an angle of $67^{\circ}$67∘ with the ground.

Work out the length of the ladder, giving your answer correct to 3 significant figures. (3 marks)

Work out the length of $x$x in a right-angled triangle in which the side opposite the $30^{\circ}$30∘ angle is $x$x and the hypotenuse is $12$12 cm. Give your answer as an exact value. (2 marks)

Write down the exact value of $\tan 45^{\circ}$tan45∘. (1 mark)