In triangle GEF, angle G = 30° and angle F = 105°. If GF = 8 units, what is the length of segment EF? Express the answer in simplest radical form.
2006-11-29 10:08:37 · 3 answers · asked by #@&*? 3 in Education & Reference ➔ Trivia
This can be done fairly easily with the Law of Sines.
First realize that angle E measures 180 - 105 - 35 = 45 degrees.
The Law of Sines says
sin45 / 8 = sin30 / x ... where x is the length of EF.
So (SQR(2)/2) / 8 = (1/2) / x
Cross-multiplying, you get (SQR(2)/2)x = 4
Multiply by 2/SQR(2). You get
x = 8 / SQR(2)
Simplify by multiplying by SQR(2) / SQR(2)
You get x = 4SQR(2), that is 4 times the square root of 2.
2006-11-30 12:32:35 · answer #1 · answered by dmb 5 · 1⤊ 0⤋
it's the magic it holds, without magic the length of the wand means nothing
2016-05-23 03:06:55 · answer #2 · answered by Anonymous · 0⤊ 0⤋
4.6
tan 30= ef/gf
ef=gf *tan30=4.6units
2006-11-29 10:19:44 · answer #3 · answered by shogunly 5 · 0⤊ 1⤋