Question

I really really need help with this question and its timed. I cant figure it out! Please help.
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

Please , i really need help. Its timed and i am absolutely clueless on how to do this. I am reading over my textbook over and over again and i cant figure it out.

Answer 2

Okay' I'll try solving it if I can.

Answer 3

Okay, thanks so much

Answer 4

Now try this.

1. Sin30 = BC/AB
Recall than Sin30 is 1/2, substitute the value,
1/2 = 41/AB
Cross multiply
AB = 2*41 = 82 feet
So, AB = 82 feet.

So the length of the hypotneuse is 82 feet.

2. Take Sin60 = AC/AB
Recall that Sin60 = Square root 3/2
Substitute the value down
Square root 3/2 = AC/82
Cross multiply
82*Square Root 3/2 = AC
41*Square Root 3 = AC
Know that Square Root of 3 = 1.73
Substitute
41*1.73 = 70.93 = AC

So, AC = 70.93 feet

Answer 5

a. So, length of the side opposite to the 60 degree angle = 70.93 feet.

b. Length of the hypotenuse of the triangular = 82 feet.

Answer 6

c. Sin30 = 41/82 = 1/2 = 0.5
Cos30 = 70.93/82 = 0.8650
Tan30 = 41/70.93 = 0.5780

Answer 7

This is the best way I think I can solve it.

Answer 8

Okay, thanks . I just dont understand the whole conspet of it

Answer 9

Since it's the special 30 - 60 right triangle
Hypo. length : 2 * 41 = 82 ft
The longer leg: √3 * 41 = 70 ft

Answer 10

Comparing with:
sin 30 = Op./ hyp = 1/2
-> hyp = 2 * 41 = 82 ft
Cos30 = Adj / hyp = √3/2
-> Adj = √3/2 * 82 = 70 ft
Tan30 = Op/ Adj = √3/3