# Calculate Area Difference of Triangles ABC with AB=5cm, AC=3.2cm

• seboastien
In summary, the question is asking for the difference between the areas of two different triangles (ABC and ADC) with the given measurements of AB=5cm, AC=3.2cm, and angle ABC=35 degrees. Some clarification is needed on the relationship between the two triangles, as it is unclear whether they have the same or different sides and angles. It is important to draw the figure and consider the different possibilities in order to find the correct solution.

#### seboastien

soine cosine rule

I have a question for you, I came across this question while revising for my exam on monday if anyone can answer this I'll be very impressed.

Two different trangles ABC have AB=5cm, AC=3.2cm and angle ABC=35degrees
calculate the difference between their areas.

Welcome to the PF, seboastien. I've moved your post from the General Math forum to the Homework Help forums. An important rule here is that homework/coursework (/revising/studying) questions must be posted here in Homework Help.

Also, we do not give out answers to these types of questions. We do provide tutorial help, to help you to figure out the problem on your own. We need to see some of your own work, though, before we can help you.

So, what are your ideas on how to approach this geometry problem? Why would the two triangles have different areas if they have two equal sides and an equal inclusive angle?

Which is the OTHER triangle? You want just the difference between a triangle and itself?

who said that the sides were the same length? AB=5 and AC=3.2, who said they were the same?
and to symbolipoint, that is the whole question which is why it makes no sense

seboastien said:
who said that the sides were the same length? AB=5 and AC=3.2, who said they were the same?
and to symbolipoint, that is the whole question which is why it makes no sense

It sounds to us like you are saying that both triangles have AB=5, and both have AC=3.2, and both have the same inclusive angle. That sounds like the triangles are equal. What are we missing?

the angle of BAC and the side BC, are saying that they are describing two seprate triangles?

What is the original question?

two different triangles ABC have AB=5cm AC=3.2cm and angle ABC=35 degrees
calculate the difference between the two sides

it still doesn't make any sense, if the triangles are seprate then their area is exactly the same surely, using the sine rule you can find the angle C, then you could find A as you know the two other angles meaning there's only one possible answer for the area

Angle ABC isn't the inclusive angle. Given the two sides you are given and the angle you are given, how many possible triangles are there? Can you draw it or them? Hint: Try both obtuse and acute triangles. Then, ask yourself what information you would need to find the area of each.

Draw the segment AB. Now though point B draw a line that makes an angle of 35 degrees to the segment. The only requirement for point C is that it lies on the line and is 3.2cm from point A. So make a circle around point A of radius 3.2cm. The circle hits the line in two points, see?

seboastien said:
it still doesn't make any sense, if the triangles are seprate then their area is exactly the same surely, using the sine rule you can find the angle C, then you could find A as you know the two other angles meaning there's only one possible answer for the area

Hi seboastien...It does make sense if the angle is at B
Draw a line AB of length 5cm, then from point A construct a circle of radius 3.2cm, Then draw a line from B inclined at 35degs from AB and see what you get.

what do you mean inclusive angle

i understand what your saying but i still appear to be getting the wrong answer

according to the textbook te answer is 4.07 cm sqrd but I'm getting 2.somthing

## Homework Statement

two different triangles ABC where AB=5cm, AC=3.2cm, and angle ABC is 35 degrees, calculate the difference between the two areas

SinA/a=SinB/b
Area=0.5abSinC

## The Attempt at a Solution

drawn line AB then a line at B 35 degrees to AB. then drawn a circle of centre A with a radius 3.2cm, I now have two triangles, one with both sides 3.2cm and the angle between 81.4
the other triangle with sides 1.8cm and 5.5cm and the angle between being 35
using Area=0.5abSinC I have found areas of both triangles and then I have found the difference between them, and I am getting the wrong answer

How can anyone tell unless you post your incorrect solution?

if you read my new "thread" as it were you will find my working

it's half ten in the evenong here, and I should probably get some kip. thanks anyway

I'm not finding any 81.4 angles. I would suggest you drop a perpendicular from A to the line BC and find it's length. Then you can just work with right triangles. Makes things easier for me, anyway. BTW the difference area you want to find is just the area of the isosceles triangle, isn't it? You don't really have to do two triangles.

seboastien said:
if you read my new "thread" as it were you will find my working

"Isosceles Triangle" -- the two triangles idea is much more sensible than I thought. Point C for ABC can be in either of two places, forming two different triangles. Tricky unless one actually draws the figure and thinks.

## 1. How do you calculate the area difference of triangles ABC with AB=5cm and AC=3.2cm?

To calculate the area difference of triangles ABC, you first need to find the area of the two triangles. The formula for finding the area of a triangle is 1/2 * base * height. In this case, the base is AB and the height can be found by using the Pythagorean theorem with AC as the hypotenuse. Once you have the area of both triangles, you can subtract them to find the area difference.

## 2. What units will the area difference be in?

The area difference will be in square centimeters (cm2).

## 3. What if the triangle is not a right triangle?

In order to find the area difference, you will still need to use the formula for finding the area of a triangle. However, instead of using the Pythagorean theorem to find the height, you will need to use the formula for finding the height of a triangle with known sides, such as Heron's formula or the Law of Cosines.

## 4. Can the area difference be negative?

Yes, the area difference can be negative. This would mean that the second triangle has a larger area than the first triangle.

## 5. Can this calculation be applied to any two triangles?

Yes, this calculation can be applied to any two triangles as long as you have the measurements for their sides. However, it is important to note that the triangles must have the same base in order for the area difference to be meaningful.