Question

A 30 degree right triangle that has a hypotenuse of 16 has an area of 64*sqrt(3) true or false

Answer 1

False

Explanation:

-We apply the Law of Sines to determine the two remaining sides:

`(a)/(Sin \ A)=(b)/(Sin \ B)=(c)/(Sin \ C)\\\\(16)/(Sin \ 90\textdegree)=(b)/(Sin \ 30), Sin \ 90\textdegree=1\\\\b=16Sin \ 30 \textdegree=8\\h=16Sin 60\textdegree=13.86`

#We use the calculated height and base dimensions to find it's area:

`A=(1)/(2)bh\\\\=0.5* 8* 13.86\\\\=55.44\`

`55.44\\eq 64√(3)`

Hence, False(the calculated area is not equal to the stated area).