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.

Answer 1

\[\tan \theta = \frac{ opposite }{ adjacent }\]Since the side that measures 41 feet is opposite of the 30 degree angle, it will be adjacent to the 60 degree angle.

So you know tan(60), and you know that the adjacent side is 41. Now just solve \[\tan30=\frac{ x }{ 41 }\]

Answer 2

how would I check my answer?

Answer 3

Well, what answer did you get?

Answer 4

Opps, when I wrote tan 30 up there I meant tan 60. I apologize for the confusion.

Answer 5

i'm almost positive it isn't right.....
ok.. hang on

Answer 6

60=x/41 is my formula, right?

Answer 7

tan 60 = x/41

It's a trigonometric function.

tan(60) = Sqrt(3)

Answer 8

1.37?

Answer 9

No.\[\tan60=\frac{ x }{ 41 }\]\[41 \times \tan 60=x\]\[41 \times \sqrt{3}=x\]\[x \approx 71.0141\]

Answer 10

Make sense?

Answer 11

yes, I think so...

Answer 12

thanks...

Answer 13

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

Answer 14

Ok.

I think these equations will help you out a lot:\[\sin A = \frac{ opposite }{ hypotenuse }\]\[\cos A = \frac{ adjacent }{ hypotenuse }\]\[\tan A = \frac{ opposite }{ adjacent }\]

Since you want to know the hypotenuse, you'll want to use either sin or cos. It doesn't matter which you use, as long as you know which angle and side to use it on.

But in your problem statement, you're given that the side that is 41 is opposite the 30 degree angle, so why not use sin(30)=41/x?

Answer 15

82?

Answer 16

Yep! :D

Answer 17

thanks... one more....

Answer 18

Ok

Answer 19

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

Answer 20

sin30 =1/2
cos30=Sqrt(2)/2
tan30=Sqrt(3)/3

Can you put those into decimal forms?

Answer 21

sin30=.5000
cos30=.8660
tan30=.5773

Answer 22

Yes, almost.

tan30=.5773503...

So when rounding you would say tan30=.5774
Other than that, everything you have is correct.

Sorry about the long delay, my internet went out for a few minutes.