Draws a triangle based on 3 side lengths.  Randomises asking angle or side.

Draws a triangle based on 3 side lengths.  Randomises asking angle or side.

Two questions testing the application of the Sine Rule when given two angles and a side. In this question, the triangle is always acute.

Two questions testing the application of the Cosine Rule when given two sides and an angle. In these questions, the triangle is always acute and both of the given side lengths are adjacent to the given angle.

Calculate the distance between two points along the surface of a sphere using the cosine rule of spherical trigonometry. Context is two places on the surface of the Earth, using latitude and longitude.

The question is randomised so that the numerical values for Latitude for A and B will be positive and different (10-25 and 40-70 degrees). As will the values for Longitude (5-25 and 50-75). The question statement specifies both points are North in latitude, but one East and one West longitude, This means that students need to deal with angles across the prime meridian, but not the equator.

Students first calculate the side of the spherical triangle in degrees, then in part b they convert the degrees to kilometers. Part a will be marked as correct if in the range true answer +-1degree, as long as the answer is given to 4 decimal places. This allows for students to make the mistake of rounding too much during the calculation steps.

Simple trig equations with radians

Draws a triangle based on 2 angles and a side length.

This is a copy of a question by Ben Brawn. It replaces the JavaScript construction of the diagram with Eukleides.

This is a copy of a question by Ben Brawn. It replaces the JavaScript construction of the diagram with JSXGraph+JME.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Draws a triangle based on 2 angles and a side length.

Draws a triangle based on 2 angles and a side length.

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Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

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resultant force

This is a set of practice questions for the non-right-angle trig component of the Australian year 12 Mathematics Standard 2 course.

It asks questions about

• finding sides and angles of right angle triangles,
• finding areas of triangles,
• using the sine rule,
• using the cos rule,
• bearings, and
• radial surveys.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Three equilateral triangles are divided equally into 3, 4 and 5 parts respectively. Calculate the distance between two marked points.

Based on a puzzle by Catriona Shearer, shared on Twitter.

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Two questions testing the application of the Sine Rule when given two angles and a side. In this question, the triangle is always acute.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Find the cosine of the angle between two pairs of 3D and 4D vectors.

The calculations and answers are correct, however the Advice should display the interim calculations of the lengths of vectors and their products to say 6dps. At present the student may be mislead into using 2dps at each stage - the instruction at the start of Advice is somewhat confusing.

Intersection points, tangent vectors, angles between pairs of curves, given in parametric form.

Questions on right-angled triangles asking for the calculation of angles using inverse-trigonometrical functions.