# math (geometry)

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

• math (geometry) -

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) -

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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