## anonymous 4 years ago This question is for trigonometry. I will type the question first and then draw the picture that goes with the problem. A two person tent is to be made so that the height at the center is a=5 feet. If the sides of the tent are to meet the ground at an angle @=30 degrees, and the tent is to be b=9 feet in length, how many square feet of material will be needed to make the tent?

1. anonymous

|dw:1327537750183:dw| So the problem is like this?

2. anonymous

|dw:1327537850715:dw|

3. anonymous

ok that makes more sense

4. anonymous

|dw:1327538013379:dw|

5. campbell_st

find the hypotenuse of the end using Sin30 = 5/h or h = 5/sin(30) h should be equal to 10ft... 2 rectangles 10 x 9 will give the answer so lond as the tent does't have a floor

6. anonymous

My apologies. I forgot one part that is with the question. Assume that the tent has a floor and is closed at both ends and give your answer in exact form.

7. anonymous

first lets slove this sense you can see that it is a isolated triangle and it is cut in half. so it is a 90-60-30 triangle and the hieght is 9 which you can get that the shorter side is 3sqrt(3) and then the hypotenuse is 6sqrt(3)

8. anonymous

then 6sqrt(3)*6=36sqrt(3)*2(cuz there are two big rectangles)

9. anonymous

The center equals 5 (where the right angle is at). The rectangle length equals 9. Sorry. The "a" and "9" look the same in the drawing.

10. campbell_st

look at the triangular end..... |dw:1327538126180:dw| tan30 = 5/x x =5/tan30 $5/\tan(30) = 5\sqrt{5}$ double it to get the width of the tent.... $10\sqrt{?}$ Areas: Triangular ends (1/2 x 5 x 10sqrt(5) ) x 2 Floor (10sqrt(5) x 9) sloping sides....see above

11. anonymous

Would x= 5$\sqrt{3}$ and the hypotenuse would equal 10?

12. anonymous

x equal 5 Squareroot 3

13. campbell_st

thats right... my typo

14. anonymous

For the rectangles, I would do 2(10)+2(9)=38. Since there are three rectangles (sides and floor), I multiply 38 x 3=114. For the triangles, how do I addd together the numbers I figured out for the hypotenuse and the sides? Do I add the 5 square root 3 together, add the two hypotenuse together and then multiple each answer by two since there's two triangle areas (front and back of tent).?