Posted by **sarah jane** on Friday, January 1, 2010 at 10:13pm.

find the perimeter of a 30-60-90 degree triangle whose shorter leg is 16 cm

- math (geometry) -
**MathMate**, Friday, January 1, 2010 at 10:43pm
The shorter leg is adjacent to the 60° angle.

We know from trigonometry that

sin 60° = 1/2

tan 60° = √3

Therefore:

adjacent side, A = 16 cm

opposite side, O = 16 tan 60° = 16√3

hypotenuse, H = 16 /sin 60° = 32

The perimeter is the sum of the three sides, namely

perimeter = A+O+H=16(3+√3)

- math (geometry) -
**Reiny**, Saturday, January 2, 2010 at 1:25am
A 30-60-90 triangle has sides 1, √3 and 2 for a perimeter of 3+√3

since the shorter side of your triangle is 16, the perimeter must be 16 times as large or 48 + 16√3

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