Use Pythagoras' Theorem to find the length of a side on a right-angled triangle.

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

This question demonstrates how to construct a JSXGraph diagram using JessieCode.

The construction shows a triangle and its orthocentre, circumcentre and centroid. They are always collinear. You can move the vertices of the triangle.

A right-angled triangle is displayed either pointing left or right with one of the other angles and one of the sides given. Use SOH CAH TOA to find the side indicated with an x.

Find the reactions of a rigid body (a triangular plate) at a pin and roller.  The load is at an angle.

Calculating the missing side-length of a triangle using the cosine rule.

Given two angles and a side-length of a triangle, use the sine rule to calculate an unknown side-length.

Students are given a diagram with 2 triangles. They are given 2 randomised lengths, and a randomised angle of depression.

They need to compute an angle by subtracting the angle of depression from 90°. Then they need to use the sine rule to calculate a second angle. Then they need to use the alternate angles on parallel lines theorem to work out a third angle. They use these to calculate a third angle, which they use in the right-angle triangle with the sine ratio to compute the third side. They then use the cos ratio to compute the length of the third side.

Students are given 2 right-angle triangles - two ramps of differing steepness up a step, and are asked to find one of a selection of randomly chosen lengths. The height of the step is given - it is randomised. Students are also given either the angle of incline of the steeper ramp or its length, both of which are randomised. They are also given the angle of incline of the shallower ramp, which is also randomised.

The student is given a triangle with one side running N-S. They are given bearings for the other two sides. They are given the length of the N-S side.

The bearings and the length are randomised.

They are then asked to find the area and the perimeter of the triangle.

Students are given the bearings and distances of 2 consecutive straight line walks. They are asked to find the distance from the starting point to the endpoint. They are given a diagram to assist them.

The bearings and distances are randomised (any bearing, distances between 1.1 and 5.). Bearings can be given as either compass bearings or true bearings.

Students are given the bearings and distances of 2 consecutive straight line walks. They are asked to find the distance from the starting point to the endpoint. They are given a diagram to assist them.

The bearings and distances are randomised (any bearing, distances between 1.1 and 5.). Bearings can be given as either compass bearings or true bearings.

Students are shown one of 5 different radial surveys and asked to answer one of 8 questions about it.

2 questions ask for the length of a side.

2 questions ask for the value of an angle.

2 questions ask for the area of a triangle.

1 question asks for the land area, and 1 question asks for the land perimeter.

The values are hard coded. In cases where your choice of precision affects your answer, a range of answers is accepted, and a comment is made in the advice to that effect.

Student is given a triangle with the value of 2 sides and 1 or 2 angles and asked to find the value of the third side using the cosine rule. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.

Student is given a triangle with the value of 3 sides and asked to find the value of an angle. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.

Student is given a triangle with the value of 1 side and 2 or 3 angles and asked to find the value of another side. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.

Student is given a triangle with 2 or 3 side lengths given and asked to use the sine rule to find the value of an angle. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.

Students are shown a right angled triangle and asked to find the value of an angle using a trig identity.

The triangle is a fixed image, but the angles and side lengths are randomly selected.

The angle is to be given in degrees and minutes.

There are 4 orientations of the triangle in the diagram. The orientation is randomly chosen.

Students are shown a right angled triangle and asked to compute a side length using a trig identity.

The triangle is a fixed image, but the angles and side lengths are randomly selected.

The angle is given in degrees and minutes, and students are asked for the side length correct to 1 decimal place.

There are 4 different triangle orientations that can display.

Given two side-lengths and an angle of a triangle, use the sine rule to calculate an unknown angle.

Calculating a section of a sector of a circle when given the arc length and angle of the sector of the circle. This question requires the use of the formulas to find the area of a sector of a circle and to find the area of a triangle. 

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.

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

Draws a triangle based on 3 side lengths.
NOT ACCESSIBLE

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

A question testing the application of the Cosine Rule when given two sides and an angle. In this question, the triangle is always obtuse and both of the given side lengths are adjacent to the given angle (which is the obtuse angle).

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.

Solve for an angle which will result in equilibrium for a triangle subjected to three couples.   A trial and error solution is recommended.

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.