geometry help

emmakatecumbo · 2017-10-30 14:20:30

I need help on these few problems i got wrong. I put teachers comments down below.

8. Each set of numbers below represents the lengths of three line segments.
Which set represent line segments that could be connected to form a triangle? Give the reasoning or show your work to support your choice
A. (3, 5, 7)
B. (3, 4, 8)
C.(1, 4, 6)
D. (1, 3, 5)
E. (5, 6, 11)
F. (1, 10, 20)

9. Each set of numbers below represents the lengths of three line segments.
Which set represent line segments that could be connected to form a triangle? Give the reasoning or show your work to support your choice
A. (2, 2, 5)
B. (5, 4, 1)
C.(5, 10, 15)
D. (7, 10, 16)
E. (2, 3, 5)
F. (5, 10, 25)

19. Here are two triangles. I am trying to measure the area of triangle ABC. The formula for area of a triangle is
base*height/2.

I know the base, but I need to find the height. I know the top of triangle ABC is directly above a point 4.5 units from point A. I also know that

What is the triangle's height? 19.31 square units

20. The sun is shining and I am on a hill. I want to measure the height of a tree downhill from me, using my one-meter stick, and a tape measure for measuring shadows. What do I do to take the slope of the hill into account? Not possible

Teacher Comments on work :

#8-9 incorrect... what is the RULE?
#19 this is the AREA... use it to find the HEIGHT... show all work
#20 this is just asking if you need to do anything special to take slope into account when you and the tree are on the SAME hill

zetafunc · 2017-10-30 20:25:27

Hi emmakatecumbo,

Let's start with the first question. In any triangle, the sum of any two sides must be longer than the third side. (This is called the triangle inequality.)

For example, (3,5,7) can be a triangle, because:

3 + 5 > 7
3 + 7 > 5
5 + 7 > 3

Can you do the rest?

emmakatecumbo · 2017-10-31 13:42:06

So number 9 would be D.
7 + 10 > 16
10 + 16 > 7
16 + 7 > 10

zetafunc · 2017-11-06 01:02:04

Correct! How about the others?

emmakatecumbo · 2017-11-06 02:53:49

I don't know how to do number 19. and 20

zetafunc · 2017-11-06 05:09:45

It looks like you are missing part of the question for #19.

Monox D. I-Fly · 2019-02-03 20:07:42

I was scavenging old questions and found the question #20. Wanna put it in the student worksheet I make but I have no idea what is the correct answer. What is it?

Jai Ganesh · 2019-02-04 00:03:15

Hi Monox D. I-Fly,

Searched for the problem and solution.

The sun is shining and I am on a hill. I want to measure the height of a tree downhill from me, using my one-meter stick, and a tape measure for measuring shadows. What do I do to take the slope of the hill into account?
A. Bend the meter stick.
B. Place the meter stick on the hill.
C. Call your mother.
D. Using the meter stick and the tape measure, recreate the slope
E. It's not possible.
F. You don't need to do anything different so long as your meter stick is on the same slope as the tree.

F is almost right, and is the nearest thing to a correct answer. What would make it correct would be the restriction that the two shadows, i.e. from the meterstick and the tree must be wholly contained in the slope. That is to say that your calculations will be off somewhat if the shadow of the tree reaches beyond the base of the hill and extends onto the presumably horizontal surface of the valley beneath the hill.

.

Monox D. I-Fly · 2019-02-05 13:08:30

Ah, thank you very much, ganesh!

Bob · 2019-02-05 19:24:47

Hi Monox D. I-Fly,

If you stand close to the tree and stand the stick so that it mimics the 'lean' of the tree (if necessary as the tree may not be vertical) and not in the tree's shadow, then the tree and its shadow and the stick and its shadow make similar triangles. So, by measuring the two shadows you can calculate the height of the tree.

Bob

Monox D. I-Fly · 2019-02-05 19:49:32

Thank you, Bob!

bob bundy wrote:

(if necessary as the tree may not be vertical)

Ah, this reminds me to when I and my friends were lost in a mountain. Almost no tree was vertical there. However, I, not even realizing that I was lost due to trusting my experienced friends, thought that such thing was normal.

gucci_venus · 2020-05-28 14:24:26

Hi,
I need help to use this formula in these questions.
Formula:
Find the measure of one base angle.
central angle = 360/9 = 40
2 * side angle + central angle = 180
2 * side angle + 40 = 180
2 * side angle = 140
side angle = 70°

Use a trig ratio to find the height of one triangle.
tan(70°) = h/(8/2)
h = 4*tan(70°)
h = 10.99 in

Use A = 1/2 bh to find the area of one triangle.
A = 1/2 (8)(10.99)
A = 43.96 in2

Find the area of the entire polygon.
A = 43.96*9
A = 395.64 in2

Questions:
1. An equilateral triangle with a side of 1 inch
3. A regular pentagon with a side of 3 centimeters

4. A regular hexagon with a side of 10 cm

5. A regular heptagon with a side of 7 inches.
Please help me ASAP!!

Bob · 2020-05-28 20:47:23

hi gucci_venus

If a polygon is regular that means all its sides and angles are the same. The formula you give is for a 9 sided regular polygon.

Sketch your polygon inside a circle. If you draw lines radiating out from the centre to each vertex, you are dividing the shape into 9 identical isosceles triangles. You can calculate the area of one triangle by finding its height and then area = half base x height. Then you can get the area of the polygon by multiplying by 9.

Q1. For an equilateral triangle the central angle is 360/3. Use that to calculate one of the base angles of one of the smaller isosceles triangles. If you then make a right angle by splitting the isosceles triangle in half, you can use the tangent formula to get the height of the triangle. Then 0.5 x base (the side of the original polygon) x height and you have one of the three identical isosceles triangles.

Q3. Same again starting with 360/5.

and so on.

The general steps are as follows:

(1) Check it is a regular polygon with N sides, each length s.

(2) Calculate the central angle by 360/N = let's call this 'a'.

(3) Calculate one base angle by b = (180 - a)/2

(4) Height, h = s/2 times tan(b)

(5) Area of one triangle, T = 0.5 x s x h

(6) Area of polygon, P = N x T.

Hope that helps.

Others have asked similar questions so you might find more examples with worked numbers if you search.

Bob

Math Is Fun Forum

#1 2017-10-30 14:20:30

geometry help

#2 2017-10-30 20:25:27

Re: geometry help

#3 2017-10-31 13:42:06

Re: geometry help

#4 2017-11-06 01:02:04

Re: geometry help

#5 2017-11-06 02:53:49

Re: geometry help

#6 2017-11-06 05:09:45

Re: geometry help

#7 2019-02-03 20:07:42

Re: geometry help

#8 2019-02-04 00:03:15

Re: geometry help

#9 2019-02-05 13:08:30

Re: geometry help

#10 2019-02-05 19:24:47

Re: geometry help

#11 2019-02-05 19:49:32

Re: geometry help

#12 2020-05-28 14:24:26

Re: geometry help

#13 2020-05-28 20:47:23

Re: geometry help

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