Trigonometry in right-angled triangles – Year 9 maths test to download as PDF

A right-angled triangle has sides 5 cm, 12 cm and 13 cm. The angle \(A\) is opposite the side of 5 cm.

1. Write down \(\sin A\), \(\cos A\) and \(\tan A\) as fractions. (3 marks)
2. Find angle \(A\) to 1 decimal place. (1 mark)

A right-angled triangle has a hypotenuse of 12 cm and an angle of \(35^\circ\).

1. Find the side opposite the \(35^\circ\) angle. (2 marks)
2. Find the side adjacent to the \(35^\circ\) angle. (2 marks)

Find the angle \(\theta\) in each right-angled triangle, to 1 decimal place.

1. Opposite 7 cm and adjacent 9 cm. (2 marks)
2. Adjacent 11 cm and hypotenuse 15 cm. (2 marks)

A 6 m ladder leans against a wall. It makes an angle of \(70^\circ\) with the ground.

1. How high up the wall does it reach? (2 marks)
2. How far is the foot of the ladder from the wall? (2 marks)

Sam stands 45 m from the foot of a tower and measures the angle of elevation of the top as \(28^\circ\). His eyes are 1.6 m above the ground.

1. Find the height of the tower above Sam's eye level. (2 marks)
2. Find the height of the tower above the ground. (1 mark)
3. The tower is really 30 m tall. Find the angle of elevation from a point 45 m from the foot, using eye level at the ground. (1 mark)