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Math help please!

Renae

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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!!!

.36 miles is what I got but the description of the problem is a bit lacking
 
That looks right.

You do have to assume a cone, which makes the "mountain" in the problem whacky. That makes me wonder if something is missing...
 
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.

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
 
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!!!

You can resolve this into simple trig by finding the radius from the circumference of 2 miles, 2*pi*r = circumference so r = 2/(2*pi).

You can now create a triangle with angles 90, 60 and 30 and the base is 1/pi.

Trig the upright using tan30 and then multiply by 3.

I think.
 
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
 
wp_20170731_21_43_48_pro.jpg

I think this is right. You need to remember SOH CAH TOA. You can solve it using cosine twice and pythagorean theorem once.
 
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.
 
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

Height of a mountain is generally stated relative to sea level so I gave up not knowing the height, above sea level, of the mountain's base. ;)
 
Valid. Basically the same as Phys got.

I still think there's an element missing and we are assuming a perfect cone.

Yeah, that's what threw me off when I first read it. Usually a mountain is a pyramid, but she didn't say perimeter. She said circumference. So, we must assume a cone. I guess.
 
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' .
 
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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.

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.
 
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' .

I get that, and I go all sorts of equations, geometry and triangles and the like were NEVER a strong suit. Adiabatic lapse rates? Sure thing, figuring out the angles of a triangle....
 
Valid. Basically the same as Phys got.

I still think there's an element missing and we are assuming a perfect cone.

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:

example.jpg

But ask me to figure out radius, heights, or triangle math and my eyes glass over.
 
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.
 
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.

It's perfect, I am very grateful really. My science background is weather, and we really don't mess with trig or geometric shapes so much as a rule. It's also been quite a while since I tried to do that kind of math.
 
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

...And if you have a picture, you need crayons. It's fundamental.
 
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.

Wow, that's meteorology stuff. One of the tools used for forecasting severe weather.
 
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