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I'm not good with this stuff, I'm really not.
I need the HEIGHT of a mountain, if it has 60 Degree angles, and 2/3rds of the way up the circumference is 2 miles, and the base radius. My math keeps coming up with not right numbers. I'd be forever in the debt of the person that can answer this.
THANK YOU!!!
If I'm reading this right, the problem assumes that the mountain is cone-shaped, and the angle between the base radius and the slant height is 60 deg. Then:
C(2/3 of the way up) = 2 mi.
C(base) = 6 mi. (the circumference is proportional to how far down the cone you go)
r(base) = 3/pi mi. (C = 2*pi*r)
h = 3*sqrt(3)/pi, or about 1.65 mi. (30-60-90 triangle)
I could explain this better with a piece of paper. It's harder to just try to type it.
I'm not good with this stuff, I'm really not.
I need the HEIGHT of a mountain, if it has 60 Degree angles, and 2/3rds of the way up the circumference is 2 miles, and the base radius. My math keeps coming up with not right numbers. I'd be forever in the debt of the person that can answer this.
THANK YOU!!!
I got a height of 8740 feet.
Basically
Circumference of 2 miles = (2)5280
So, 5280 = pi R ---> R=1682 Feet
Then, For height of upper third of the mountain,
Tan 30 Deg = 1682/x ----> x = 2913 feet
So, for the whole height of the mountain,
3x = 8739 feet
I got a height of 8740 feet.
Basically
Circumference of 2 miles = (2)5280
So, 5280 = pi R ---> R=1682 Feet
Then, For height of upper third of the mountain,
Tan 30 Deg = 1682/x ----> x = 2913 feet
So, for the whole height of the mountain,
3x = 8739 feet
Valid. Basically the same as Phys got.
I still think there's an element missing and we are assuming a perfect cone.
View attachment 67220755
I think this is right. You need to remember SOH CAH TOA. You can solve it using cosine twice and pythagorean theorem once.
My wife likes your method the best. Screw her .
That's hilarious! Can I quote you?
If I'm reading this right, the problem assumes that the mountain is cone-shaped, and the angle between the base radius and the slant height is 60 deg. Then:
C(2/3 of the way up) = 2 mi.
C(base) = 6 mi. (the circumference is proportional to how far down the cone you go)
r(base) = 3/pi mi. (C = 2*pi*r)
h = 3*sqrt(3)/pi, or about 1.65 mi. (30-60-90 triangle)
I could explain this better with a piece of paper. It's harder to just try to type it.
I'm going to break this into parts with my Geometry wife driving .....
Breaking into thirds, the circumference at the base is 3 times the circumference 2/3 of the way up; solve for circumference.... 6 miles...
Circumference = 2 (pi) radius; solve for radius at base.....0.955 miles
Using a right angle, with 60[SUP]o[/SUP] lower left, 30[SUP]o[/SUP] at the top and 90[SUP]o[/SUP] for the right angle;
use tangent of 60 = opposite over adjacent (TOA); tan 60 = height/radius;
solve for height; h = tan 60 times radius = (tan 60) [SUP].[/SUP] (0.955 miles) = 1.65 miles ;
1.65 miles times 5,280 feet/mile = 8,733 feet with no rounding in the problem; perfect significant figures;
As you're seeing Renae, there is no ONE way to do this; that's the beauty of math, especially when used as 'the language of science' .
Valid. Basically the same as Phys got.
I still think there's an element missing and we are assuming a perfect cone.
I'm not good with this stuff, I'm really not.
I need the HEIGHT of a mountain, if it has 60 Degree angles, and 2/3rds of the way up the circumference is 2 miles, and the base radius. My math keeps coming up with not right numbers. I'd be forever in the debt of the person that can answer this.
THANK YOU!!!
6 miles, I like it.
I'm writing a novel. And the capitol of my fantastical kingdom is built on a mountain that's been lopped off 2/3 of the way up. I for the life of my couldn't get the math to come up right, somehow I came up with 33 miles and 99 mile radius, which told me I better stop trying to do math. I like that, 6/2 ratio is perfect. It's not a natural formation, fickle Gods and their powers and all tend to make impossible realities, thank you for figuring that math out for me.
That's cool. I wondered what was behind the question.
I'm a techie, but I didn't even bother to solve it after I saw Phys' answer. Thinking through what he did, it had to be basically right unless a calculation was wrong.
As you've seen, there are many ways one can solve the same problem.
She said the base was the radius which I took to mean the base of the mountain was the radius of the circle putting it at .32 miles and then the Pythagorean theorem for the height.This really needs a picture
It was, but the top got lopped off, smooth as a pool table. Big city built on it, very fancy and mystical stuff, that's easy. Trig and Geometry and crap? No thank you.
I can read this:
View attachment 67220759
But ask me to figure out radius, heights, or triangle math and my eyes glass over.
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