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Pupils should be taught to apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in 2 {and 3} dimensional figures

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

• Make Them Right Arrange the measurements next to the sides of the triangles so that each diagram is correct according to Pythagoras' Theorem.
• Which Side? Arrange the diagrams in groups depending on whether the arrow is pointing to the opposite, adjacent or hypotenuse.
• Trigonometry Video The basic trigonometric ratios are sine, cosine and tangent and are used to find the lengths of sides and the size of angles in right-angled triangles.
• Trigonometry Sine, cosine and tangent ratios are used to find sides and angles in right-angled triangles.
• 3D Trigonometry Presentation A slide presentation (a poem) introducing using trigonometry (including Pythagoras' Theorem) to find lengths and angles on three dimensional shapes.
• Trigonometry in 3D Calculate the lengths of sides and the size of angles in three dimensional shapes.
• Three Dimensional Trigonometry Video When you have mastered trigonometry in two dimensions it is time to practise solving three-dimensional problems.

Here are some exam-style questions on this statement:

• "\(ABC\) is a right-angled triangle." ... more
• "The diagram (not drawn to scale) shows a right-angled triangle." ... more
• "An isosceles triangle shaped frame is made from four pieces of metal. The frame has a height of 8 metres and a base of length 12 metres." ... more
• "Work out the value of \(x\), the length in centimetres of one of the sides of this right-angled triangle." ... more
• "ABC is a right-angled triangle as shown in the diagram below. Calculate the length of AB giving your answer correct to three significant figures." ... more
• "An arborist sights the top of a tree using a clinometer and reads the angle of elevation to be 29^o. Her clinometer is 28 metres from the base of the tree and is on a tripod making it 1.5 metres above ground level." ... more
• "The diagram shows a right-angled triangle and a semicircle. The straight side of the semicircle is the same length as the longest side of the triangle." ... more
• "The diagram shows a trapezium where the sides AC and BD are parallel." ... more
• "Four copies of a green right-angled triangle are used to enclose a yellow square." ... more
• "Taptaya Park Tower is over two hundred metres tall. There is a zip wire from the observation deck to a point on the ground 550 metres away in a northerly direction." ... more
• "Triangle ABC has a right angle at C." ... more
• "Neung is at Bangkok's Suvarnabhumi Airport watching the planes take off. He observes a plane that is at an angle of elevation of 25^o from where he is standing at point N. The plane is at a height of 390 metres as can be seen in the following diagram (not to scale)." ... more
• "A square has sides of length \(x\) cm." ... more
• "(a) Write down the exact value of \(\tan 60^o\)." ... more
• "Rectangle ABCD is the horizontal base of a trapezoidal prism ABCDEFGH." ... more
• "The diagram shows a rectangular-based pyramid, TABCD (not drawn to scale)." ... more
• "ABC is a triangular car park on horizontal ground. The length of AB is 90m and the length of AC is 65m. The size of angle BCA is 68^o." ... more
• "The gradient of the line joining the origin to the point A is \(\frac12\)" ... more

See all these questions

Here are some Advanced Starters on this statement:

• Coordinate Distance
  Find k given that(-2,k) is 13 units away from (10,9) more
• Speed Circles
  Find the diameters of the circles in the corners of the square. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

• Trigonometry Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Pupils begin by learning the names on the sides of a right-angled triangle relative to the angles. They then learn the ratios of the lengths of these sides and the connection these ratios have with the size of the angles. Having mastered right-angled triangle trigonometry pupils then progress to more advanced uses including the sine rule and cosine rules. The use of a scientific or graphing calculator is essential for this topic and correct, efficient use of the calculator is an important skill to develop. Here's a Trigonometry Wordsearch just for fun.