Pythagoras and trigonometry in right-angled triangles – Year 11 GCSE maths test to download as PDF

A right-angled triangle has hypotenuse 13 cm and one side 5 cm.

1. Find the other side. (2 marks)
2. Find the smallest angle. (2 marks)

In a right-angled triangle, the side adjacent to a \(38^\circ\) angle is 7 cm.

1. Find the opposite side to 2 decimal places. (2 marks)
2. Find the hypotenuse. (2 marks)

A flagpole is 18 m tall. A person stands 30 m from its base.

1. Find the angle of elevation of the top of the pole. (3 marks)
2. Find the distance from the person to the top. (1 mark)

Without a calculator.

1. Write the exact value of \(\cos60^\circ\) and \(\tan45^\circ\). (2 marks)
2. A triangle has a \(30^\circ\) angle and hypotenuse 8 cm. Find the opposite side. (2 marks)

A box measures 8 cm by 6 cm by 4 cm.

1. Find the length of the longest straight rod that fits inside, to 2 decimal places. (2 marks)
2. Find the angle this rod makes with the base. (2 marks)