Question

A building lot in a city is shaped as a 30° -60° -90° triangle. The side opposite the 30° angle measures 41 feet.

a. Find the length of the side of the lot opposite the 60° angle.

b. Find the length of the hypotenuse of the triangular lot.

c. Find the sine, cosine, and tangent of the 30° angle in the lot. Write your answers as decimals rounded to four decimal places.

Answer 1

aah now we have a question
ratios are still \(1:\sqrt{3}:2\) so the measurements are
\[41,41\sqrt{3},82\]

Answer 2

The side opposite to \(30^{\circ}\) is half the hypotenuse.

Answer 3

that is \(41\) is the short sides, \(41\sqrt{3}\) is the long side opposite the 60 degree angle and \(82\) is the hypotenuse

Answer 4

So it's basically \(x,x\sqrt{3},2x\)

Answer 5

@satellite73: My four legs say that you named them sides.

Answer 6

what @ParthKohli said
udderly true

Answer 7

Or you can derive everything yourself if you know that on a 30-60-90 triangle that one of the legs is half of its hypotenuse.

x, x(1/2), and by the pythagorean theroem: x(sqrt(3)/2)

Answer 8

The non-homourous version of that is -- you meant to say legs instead of sides.

Answer 9

none of you are making any sense to me

Answer 10

So start by drawing out a triangle that has angles of about 30, 60, and 90 degrees and start labeling things. We'll help you along as you need help.

Answer 11

If you multiply \(\sqrt{3}\) to the side opposite to \(30^{\circ}\), you get the one opposite to \(60^{\circ}\).
If you double the side opposite to \(30^{\circ}\), you'd get the hypotenuse's length.

Answer 12

I'm still completely lost

Answer 13

Please mention how you're stuck so we can help :)

Answer 14

I just want the answers cause i don't know how to do this

Answer 15

Too bad, we can help you but we won't do your homework for you.

Answer 16

Are you in FLVS?

Answer 17

here is the basic triangle

Answer 18

none of you are even helping me ><

Answer 19

all the ratios remain the same if you scale the triangle differently, so

Answer 20

So start by drawing out a triangle that has angles of about 30, 60, and 90 degrees and start labeling things. We'll help you along as you need help.

Answer 21

this is my best explanation, i am not sure of any other way to say it
we could derive these ratios if that would help, but the ratios always stay the same

Answer 22

I think if she draws it out for herself, it'll be easier for her to see what's going on. It's pretty crowded in here so I'm probably just going to say good luck to you all.

Answer 23

@mathgeek898 Which school are you in?

Answer 24

I already drew out a triangle I don't know how to do this and I'm having a break down

Answer 25

i have in fact written the answers, not once, but twice above. see my first post, also the second picture above

Answer 26

Alright let's just relax for a second. It's just a math problem with a dinky little triangle. If you want to understand it I am willing to take as much time as you need to help you out. Help me help you out though, I don't know what part you get stuck at.

Answer 27

Satellite73 I don't see how you gave me the answers I looked back and I am still completely confused and Kainui I'm stuck on all of it!!! I can't fina A. cause I don't know what I'm doing!!!!

Answer 28

Alright, so you've drawn out the triangle on paper, right? Now, did you label the angles correctly? Remember the smallest angle is 30 degrees, the second biggest is 60, and the largest is 90 degrees. Have you gotten to this point or does this not make sense? If so, why not?

Answer 29

I labeled everything I'm not sure it's right though

Answer 30

i see the problem
the "30" and the "60" are measure of angles, not the lengths of the sides

Answer 31

Yes they are!!!

Answer 32

it is the length of the sides that you are looking for

Answer 33

this is what I'm looking for
a. Find the length of the side of the lot opposite the 60° angle.

b. Find the length of the hypotenuse of the triangular lot.

c. Find the sine, cosine, and tangent of the 30° angle in the lot. Write your answers as decimals rounded to four decimal places.

Answer 34

you labelled the length of the hypotenuse as 90, but it is the right angle that has measure 90 degrees