m GH = 57''
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tan 39° = opposite / adjacent
tan 39° = m GH / m HJ
tan 39° * m HJ = m GH
m HJ = m GH / tan 39°
m HJ ≈ 57'' / 0.810
m HJ ≈ 70.4'' <——— measure of the segment HJ
________
sin 39° = opposite / hypotenuse
sin 39° = m GH / m GJ
sin 39° * m GJ = m GH
m GJ = m GH / sin 39°
m GJ = 57'' / 0.629
m GJ ≈ 90.6'' <——— measure of the segment GJ
________
So the perimeter is
p = m GH + m HJ + m GJ
p = 57'' + 70.4'' + 90.6''
p = 218'' <——— this is the answer.
I hope this helps. =)
Tags: perimeter right triangle sine cosine tangent sin cos tan trig trigonometry geometry