Question

The length of the hypotenuse of a 30°-60°-90° triangle is 11. What is the perimeter?

Answer 1

you can always draw it out, then do the trig right after!



if you have memorized your unit circle, you'll know that sin30=1/2 and sin60=sqrt3/2



now relating this to the triangle whose hypotenuse is 11 instead of 1, you get this:

Answer 2

wait i dont get it????

Answer 3

http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/720px-Unit_circle_angles_color.svg.png

does this help? Otherwise, where did I lose you D: I rushed a bit, but I tried to be clear! Not sure what you learned in school already though

Answer 4

maybe you know these side(opposite to 30)=hyp/2 and side(opposite to 60)=hyp*srt(3)/2

Answer 5

i am so lost!!

Answer 6

perimeter is the addition of all the sides right? The hypotenuse + short leg + long leg

with a 30-60-90 triangle such as this one, the hypotenuse is given, then using trig identities like sin(theta) = opposite/hypotenuse, you can solve for the other two side lengths.

the short leg is the leg opposite the 30 degree angle. therefore
sin(30) = shortleg/hypotenuse and the short leg = sin(30)*hypotenuse or 11*1/2=11/2

the long leg can be solved for the same way
sin(60) = longleg/hypotenues and long leg = sin60*11=11*sqrt3/2

now finally the perimeter is all of them added together

11+11/2 + 11sqrt3/2 = 3/2*11 +11sqrt3/2 = 33/2+11*sqrt3/2

Answer 7

ohhhhhhh! okay thank you i get it now

Answer 8

glad i could help :)