Question

Fill in the blanks. In the 30-60-90 triangle below, side s has a length of ___________ and the hypotenuse has a length of ____________.

Answer 1

We know that the side s divided by hypotenuse h = sin 60 degrees.\[\sin 60^\circ = \frac{s}{h}\] We also know that the side s divided by the side of length 1 = tan 60 degrees.\[\tan 60^\circ = \frac{s}{1}\]
From your knowledge of the unit circle, what are the values of \(\sin 60^\circ \) and \(\tan 60^\circ\)?

Answer 2

0.86602540378443864676372317075294 and 1.7320508075688772935274463415059?

Answer 3

well, yeah. do you know the symbolic versions?

Answer 4

no im not very good at math let alone geometry i need these answers of my class or i wont graduate high school so i need these answers quickly...

Answer 5

well, have a look at the unit circle diagram here: http://www.embeddedmath.com/downloads/files/unitcircle/unitcircle-letter.pdf

Answer 6

okay all of that looks like gibberish to me sorry...

Answer 7

anyhow, hopefully it is clear that s = sqrt(3), then
\[1^2+ s^2=h^2\]\[1^2+(\sqrt{3})^2 = h^2\]\[1+3=4\]\[h=2\]

so the sides are in ratio \(1:\sqrt{3}:2\)