# Finding length of 3 sides of a triangle

• mimi.janson
In summary, the student attempted to solve a homework problem but got confused and lost the original information. They were then able to find the solution using pythagoras. However, they were not able to solve the problem using cosinus.
mimi.janson

## Homework Statement

hi i have a photo with some given information. I need to find the length of all three sides of that triangle and also the area of the triangle

I have already found them but i get 2 different results

## Homework Equations

I have used both cosinus and pythagoras

## The Attempt at a Solution

I already got that length of AC is 20 since that's one of the given lengths. CB i got to be 42,1 and AB i sometimes get to be 19,2 when i use cosiunus, but when i use pythagoras and divide the triangle into 3 parts i get the length of AB to be 31 which is correct?

and my area is 0,5*hight*b where the hight is 3*the length of MD. so i got MD to be 9,89 and therefore my area is 0,5*29,67*20 = 296 but it just seems too big?

can anyone please check my attachment and help me out?

Last edited:
mimi.janson said:
CB i got to be 42,1 ...

How? What's your reasoning? It should be 32.6

dx said:
How? What's your reasoning? It should be 32.6

Because i first found the length of CD which i did with the sinus relation
c/sinC=d/sinD
c/sin23=10/sin67that gave me the length of MD whish is 9,8.
since i had the length of MD =9,8 and the length of MC =10 i used pythagoras 102*9,82=the length of DC.

so i got DC to be about 14 and since BC is 3 times DC i just had to say 3*14=42

did i really solve it wrong? I've been staring at it for the whole day

i don't know if it plays any role but i use degrees instead of radians

mimi.janson said:
c/sin23=10/sin67that gave me the length of MD whish is 9,8.

MD = c = 10(sin(23)/sin(67)) = 4.2

DC = √(4.22 + 102) = 10.85

BC = 3DC = 32.6

Last edited:
A simpler way to calculate DC is from the definition of cosine:

DC cos(23) = MC, so DC = MC/cos(23) = 10/cos(23) = 10.86

I see where you went wrong. When you calculated sin(23) and sin(67) on your calculator, you were in radian mode, and the calculator interpreted 23 as 23 radians, instead of 23 degrees. You should switch to degree mode.

dx said:
MD = c = 10(sin(23)/sin(67)) = 4.2

DC = √(4.22 + 102) = 10.85

BC = 3DC = 32.6

Yes i checked and it was the degrees that were the problem...im really nervous for my exams this summer, because you see i have been looking at this which should be a simple matter since they taught it to my class like 2 years ago, and i still spent like 4 hours trying to solve it because of the radians...and i never find the fail ever even though i have tons of this kind of strange fails...sometimes i even see a number wrong and sit trying to find it for hours. .. but i have changed it now and do get the results you get too.

I prefer to use pythagoras instead of cosine as much as possible because i find it hard.
I used cosine to find the length AB and got it to be 16,195

so my three lengths are now

BC=32,597
AC=20
AB = 16,195

i was just thinking does that make an area of 127,35 realistic? i said 0,5*12,735*20. I used the length by saying that it must me 3*MD

mimi.janson said:
so my three lengths are now

BC=32,597
AC=20
AB = 16,195

Looks good.

mimi.janson said:
i was just thinking does that make an area of 127,35 realistic? i said 0,5*12,735*20. I used the length by saying that it must me 3*MD
0.5*12.735*30 (not 20) is the area of the right triangle with hypotenuse BC. From that you have to subtract the area of the right triangle with hypotenuse BA.

Last edited:
dx said:
Looks good.

0.5*12.735*30 (not 20) is the area of the right triangle with hypotenuse BC. From that you have to subtract the area of the right triangle with hypotenuse BA.

ok i did so and i got 127,35

Yes, it's correct.

dx said:
Yes, it's correct.

Ok thank you so much you really made my day today <3

No problem. Good luck with your exams.

dx said:
No problem. Good luck with your exams.

thank you again and sorry i had to blabber about them i just get frustrated when doing math

mimi.janson said:

## Homework Statement

hi i have a photo with some given information. I need to find the length of all three sides of that triangle and also the area of the triangle
...

can anyone please check my attachment and help me out?

It's quite frustrating for anyone willing to help you, to see that the initial information has suddenly disappeared.

SammyS said:

It's quite frustrating for anyone willing to help you, to see that the initial information has suddenly disappeared.

oh I am sorry must have clicked something without knowing, will be more carefull next time

## 1. How do you find the length of the sides of a triangle?

The length of the sides of a triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can also be calculated using trigonometric functions if the angles of the triangle are known.

## 2. What is the Pythagorean theorem?

The Pythagorean theorem is a mathematical formula that relates the lengths of the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

## 3. Can you find the length of the sides of a non-right triangle?

Yes, the length of the sides of a non-right triangle can be found using the Law of Cosines or the Law of Sines, depending on the information given about the triangle. These laws use trigonometric functions and angles to calculate the side lengths.

## 4. What information do I need to find the length of the sides of a triangle?

In order to find the length of the sides of a triangle, you will need to know at least three pieces of information, which can include the lengths of two sides and the measure of an angle, the lengths of all three sides, or the lengths of two sides and the measure of an angle opposite one of those sides.

## 5. Is there a specific order to use when finding the length of the sides of a triangle?

Yes, when using the Pythagorean theorem, it is important to use the side lengths in the correct order, as the hypotenuse must always be the longest side. When using the Law of Cosines or the Law of Sines, you must use the corresponding angles and sides in the equations.

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