An ice cream cone manufacturer makes cones with a bottom angle of 30º. The sides of the cones are 14 cm long. Determine the diameter of the cones.
2006-06-08 14:19:23 · 7 answers · asked by idiotmatt2000 1 in Science & Mathematics ➔ Mathematics
Using cosine rule,
a² = b² + c² - 2bc cos A,
where A=30º , b and c are the sides of cone (i.e. 14cm) and a is the diameter of the cone.
a² = 14² + 14² - 2(14)(14)(cos 30º)
= 392 - 392 cos 30º
= 392- 392 (0.8660)
= 392- 339.472
= 52.528 cm
Diameter, a = 7.2476 cm
2006-06-08 14:40:57 · answer #1 · answered by triple33 1 · 0⤊ 0⤋
This is a trigonometry question. let the height of the cone, radius and the side of the cone make a right triangle
radius of th cone/ side of the cone = cos 30 degrees
radius of the cone = side of the cone * cos 30
radius = 14 * 0.866 = 12.12 cm
Diameter of the cone = 2*radius = 2*12.12cm = 24.24cm
2006-06-08 21:41:00 · answer #2 · answered by Munir B 3 · 0⤊ 0⤋
the side of the cone is the hypotenuse of a 15-75-90 triangle; the sides are the height h and the radius r
sin 15 = r / hyp = .2588 = r / 14
r = .2588 * 14 = 3.62 cm
diameter = 2r = 7.25 cm
2006-06-09 01:33:41 · answer #3 · answered by jimbob 6 · 0⤊ 0⤋
c^2 = a^2 + b^2 - 2ab cos(C)
c^2 = 14^2 + 14^2 - 2(14 * 14)cos(30)
c^2 = 196 + 196 - 2(196)cos(30)
c^2 = 392 - 392cos(30)
c^2 = 52.518
c = 7.246933326
ANS : about 7.25
2006-06-08 21:45:55 · answer #4 · answered by Sherman81 6 · 0⤊ 0⤋
i was going to guess 7cm. i liked geometry but started hating math when it got into trig and calculus.
2006-06-08 21:30:20 · answer #5 · answered by midnightrose 4 · 0⤊ 0⤋
7.25cm
2006-06-08 21:27:38 · answer #6 · answered by Jason T 3 · 0⤊ 0⤋
i have no clue.
2006-06-08 21:24:23 · answer #7 · answered by carmike_dogs 1 · 0⤊ 0⤋