Ratio of 30-60-90 degree triangles

[Guest]

hi there,

Currently reading the geometry strategy guide on page 31 and don't fully get the following information.

Ratio is: 1: square root of 3: 2 for a 30-60 & 90 degree right angle triangle.

What I don't get is when a side is given for the hypotenuse (in this case 10) how do you find the multiplier based on the ratio provided. The ratio is 5: 5(square root of 3): 10.

Can anyone please shed some light on what I may be missing?

thanks!

[guestt]

hi
i can help you find the other side by the unknown multiplier .
hi there,

In a 30-60-90 traingle the ration of sides is always this way
30-60 -90
1 - root 3 - 2
if the hypotenuese is given to be 10 means its is double of the side facing the 30 degree angle and for the side facing 60 degree angle it is divided by 10/root 3/2=5 root 3

this is how i goes
30-60 -90
1 - root 3 - 2

if for 1 it is 2
for 10 it is how much so cross multiply 10 * 1/2= 5
for root 3 it is 2
for 10 it is how much therefore cross multiply 10*root 3/2 = 5 root 3

hope that helps

[rfernandez]

I find it helpful to think of the ratio as 1x : root(3)x : 2x. If the hypotenuse is 10, then 2x=10, so the "multiplier" x is 5.

That means the side measures are 5 : 5*root(3) : 10.

[Guest]

Thanks Rey! That actually helped alot.

[StaceyKoprince]

Glad Rey could help!