i seriously need help this trig question :( any help is much appreciated <3

Question

An ice cream company is designing waffle cones to use for serving frozen yogurt. The cross-section of the design has a bottom angle of 29°. The sides of the cones are 13 cm long. Determine the radius of the top of the cone.

Answer 1

Ok the cross section is an isoceles triangle

with equal sides 13 and angle 29 in between.

Dropping the height H, from the 29 degree angle

at the tip to the opposite side creates two equal

right triangles by HL (the height is shared

leg between both right triangles and both

hypotenuse are 13)

Splitting the 29 degree angle is 14.5 degrees at the

tip of each right triangle...

That leaves 75.5 degrees for the 3rd angle..

The radius is then cos 75.5 = R/13 ---> R = 13 * cos 75.5

R=3.2549400527077384065209326535815

The height of the cone is sin 75.5 = h/13 --> h = 13*75.5

h=12.585919324915401074567298882185

Pythagorean checks out!

Answer 2

Law of Cosines

d² = 13² + 13² - 2(13)(13) cos 29°

d is the diameter.