Angles A, B and C are the angles of a triangle. Decide whether each of the following is an identity, always true for all triangles, or an equation, sometimes true. If you decide it is an equation find the solution or solutions and describe the corresponding triangle.
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The angle of elevation from a point C on the ground, at the centre of the goalpost, to the highest point A of the arc, directly above the centre of the Moses Madhiba Soccer Stadium in Cape Town, is 64.75 degrees. The soccer pitch is 100 metres long (PQ […]
The line RS is a tangent at P to the circle centre O and radius 1 unit.
Find the lengths OQ, PQ, PS, OS, OR and RP.
If OS and OR lie on the coordinate axes, what are the coordinates […]
The diagram shows three angles a, b and c.
How many ways can you prove that a + b = c?
What other interesting properties can you find?
When this activity was originally published on NRICH, two boys from Madras School in St Andrew’s, Scotland sent […]
Two flagpoles are 30 metres apart. One has height 10 m and the other has height 15 m. Two tight ropes connect the top of each pole to the foot of the other.
How high do the two ropes intersect above the ground?
How many different methods can you find to solve this problem?
The centre square has the area of 1 (one) square unit.
Draw the diagram. You can download square dotty paper here.
What is […]
The angle marked in the diagram is angle a.
Copy the diagram and find all the angles in terms of the angle a.
Find the six line segments in the diagram corresponding to sina, cosa, tana, 1/sina, 1/cosa and 1/tana.
Find the areas of […]
Make a centre crease down the length of the paper then open it up.
Next fold one corner over and onto the centre crease so that the fold line passes through the corner next to it (on the short side of the paper).
Is it possible for a tetrahedron to have edges of lengths 10, 20, 25, 45, 50 and 60 units?
Can you write general rules for someone else to use to check whether […]
If you have geometry instruments then try it for yourself. What do you notice?
Can you give reasons for your answer to the question “Is it possible?”
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