Weird Trigonometry(5)

By Dave C, 2013

Obtaining the inverse Tan without too much effort.

...in other words, getting a good approximation for the angle in a triangle given the base length and height.

dTBase

Height

57

57

1

1)45(

d

d

dTdTan

d

dTd

57

57

dT

T

d

d

1

157

2m

3m

e.g.,

1

157

d

d

T

Td

1

157

32

32

d

5

157d

O11.4 d

2m

3m

e.g.,

O11.4 d

OOO 6.33 11.4 45 angle

2m

3m

e.g.,

O11.4 d

OOO 6.33 11.4 45 angle O32-1 7.33)(Tan

Correct value:

The approximation is accurate to within 2% for all Tan values between about 0.5 and about 2.5.

That covers a broad range of triangles.

1

157 45 O

d

d

T

Tangle

%5 1

106 45 O lessT

Tangle

d

d

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