equable triangles

the proof that there are only five equable triangles (integer sided) was done in 1904

this version of a proof is largely due to David Wells with small bits of help from me

it is complex but involves only GCSE tools

circle theorems meet 0.5absinC

an idea by Martin Wilson, in Harrogate, blending the circle theorems with area

a ppt is here

you could use normal trigonometry (by bisecting chords) but Martin's intention is that students use the (more efficient) method of calculating 0.5 a b sinC

resources 2, 3 and 4 present an interesting relationship between sines
that is not easy to justify(?)
without involving the trig. formula sinA + sinB = 2sin(semi-sum).cos(semi-difference)
and noting that cosD = sin(90 - D)

there's a sequence to follow

0.5 a b sin C used to find areas of triangles

area = 1/2 a b sin C

a powerpoint 

area 5

not using right angled triangles and Pythagoras...
using:

• the cosine rule
• normal trigonometry
• area of a triangle, A = 1/2 ab sin C

sin2x